WO2022050154A1 - Optical measurement device and optical measurement method - Google Patents

Abstract

In the present invention, a beam splitter BS receives coherent light 2 as a first input and a squeezed vacuum field 4 as a second input. A first optical detector PD2 measures light 8 obtained as a result of a first output 6 of the beam splitter BS acting on a sample 1. A second optical detector PD2 measures a second output 10 of the beam splitter BS. A processing part 110 processes an output of the first optical detector PD1 and an output of the second optical detector PD2 and obtains a spectral characteristic of the sample.

Description

Light measuring device, light measuring method

This disclosure relates to optical measurement techniques such as spectroscopy and imaging.

Quantum Enhanced spectroscopy and imaging methods are attracting attention because they can obtain a higher signal-to-noise ratio (SNR) than the standard quantum limit (SQL) and can achieve higher sensitivity. [Non-Patent Document 1-3]. So far, several methods of quantum enhancement have been applied to spectroscopy and imaging. For example, entangled photons generated by spontaneous parametric down-conversion (SPDC) are used for transmission imaging [Non-Patent Document 4-7] and differential phase imaging [Non-Patent Document 8]. Tangled photons generated by a double-resonant optical parametric oscillator (OPO) are also used in spectroscopy [Non-Patent Documents 9 and 10]. Further, the amplitude squeezed light generated by displacement of the squeezed vacuum field [Non-Patent Document 11-13] or by a seeded Parametric Amplifier (OPA: Optical Parametric Amplifier) [Non-Patent Document 14-16] is spectroscopic. Used for method and imaging.

However, since relatively high optical power (10-100 mW) is required to obtain high SNR in classical spectroscopy and imaging, the SNR limit achieved in classical spectroscopy and imaging is quantum. It remains difficult to push up with the use of augmentation. In fact, conventional methods of quantum enhancement have been demonstrated with very weak optical power (<~ mW). For example, the typical average power of SPDC photons is less than picowat. In amplitude squeezing due to displacement of a squeezed vacuum field, the beam splitter (BS) used for displacement can result in significant losses. Amplitude squeeze using seeded OPA also results in significant losses as both vacuum fluctuations and seed light are attenuated by the OPA. One exception is the quantum enhanced interferometry [Non-Patent Document 17] used in the gravitational wave detector [Non-Patent Document 18-20], which is used in the unused port of the interferometer to achieve sensitivity exceeding SQL. A squeezed vacuum field is injected. However, this method is mainly used for phase measurement. Although a more advanced method can realize simultaneous measurement of amplitude and phase [Non-Patent Document 21], the configuration becomes complicated. Therefore, these methods are not immediately applicable to spectroscopy and imaging, where the intensity of transmitted light is often measured.

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The present disclosure has been made in such circumstances, and one of the exemplary purposes of that embodiment is to improve the SNR of optical spectroscopy and imaging over SQL, even when the average power of light is high (> 10 mW). To provide a spectroscopic and imaging device and method with balanced detection.

One aspect of this disclosure relates to an optical measuring device. The optical measuring device includes a light source that generates coherent light, a squeezed vacuum field generator that generates a squeezed vacuum field, and a beam splitter that receives coherent light at the first input and a squeezed vacuum field at the second input. , The first light detector that measures the light obtained as a result of the first output of the beam splitter acting on the sample, the second light detector that measures the second output of the beam splitter, and the output of the first light detector. It is provided with a processing unit that processes the output of the second optical detector and acquires the characteristics of the sample.

Another aspect of the present disclosure is an optical measurement method. In this method, a step to generate coherent light, a step to generate a squeezed vacuum field, a step to combine the coherent light and the squeezed vacuum field by a beam splitter, and the first output of the beam splitter act on the sample. The step of balancing the light obtained as a result of the above and the second output of the beam splitter is provided.

It should be noted that an arbitrary combination of the above components and a method in which the components and expressions are mutually replaced between methods, devices, systems and the like are also effective as aspects of the present invention or the present disclosure. Furthermore, the description of this item (means for solving the problem) does not explain all the essential features of the present invention, and therefore subcombinations of these features described may also be the present invention. ..

According to the present disclosure, even when the average power of light is high (> 10 mW), the SNR of optical spectroscopy or imaging can be improved as compared with SQL.

It is a figure which shows the apparatus which used the principle of QBD. 2 (a) and 2 (b) are diagrams showing a two-mode wave function Ψ (x _a , x _b ) at the input and output of the beam splitter BS in the case of balance detection without injecting a squeezed vacuum field. 3 (a) and 3 (b) are diagrams showing a two-mode wave function Ψ (x _a , x _b ) at the input and output of the beam splitter BS in the case of balance detection in which a squeezed vacuum field is injected. It is a figure which shows the SRS microscope (QE-SRS microscope) with quantum enhancement. It is a figure which shows the setup of the QE-SRS microscope. It is a figure which shows the SRS spectrum of dimethyl sulfoxide-d6 (d-DMSO). It is a figure which shows the evaluation result of squeezing when the sample is not arranged.

(Outline of Embodiment)
Some exemplary embodiments of the present disclosure will be outlined. This overview simplifies and describes some concepts of one or more embodiments for the purpose of basic understanding of embodiments, as a prelude to the detailed description described below, and is an invention or disclosure. It does not limit the size. This overview is not a comprehensive overview of all possible embodiments and is not intended to identify key elements of all embodiments or to delineate the scope of some or all embodiments. For convenience, "one embodiment" may be used to refer to one embodiment (examples or modifications) or a plurality of embodiments (examples or modifications) disclosed herein.

The optical measuring device of one aspect of the present disclosure includes a light source that generates coherent light, a squeezed vacuum field generator that generates a squeezed vacuum field, and a squeezed vacuum that receives coherent light at the first input and squeezed vacuum at the second input. A beam splitter that receives a field, a first light detector that measures the light obtained as a result of the first output of the beam splitter acting on the sample, a second light detector that measures the second output of the beam splitter, and a first. It is provided with a processing unit that processes the output of the optical detector and the output of the second optical detector and acquires the characteristics of the sample.

According to this configuration, even when the average power of light is high (> 10 mW), the SNR of optical spectroscopy and imaging can be further improved compared to SQL. Examples of sample characteristics include sample transmittance, loss, reflectance, and gain.

In one embodiment, the processing unit may weight and subtract the output of the first photodetector and the output of the second photodetector.

In one embodiment, when the transmittance of the beam splitter is T ₁ and the transmittance of the path of the second output of the splitter is T ₂ , the weighting coefficient for the output of the first photodetector is (1-T ₁ ). Substantially proportional, the weighting factor for the output of the second photodetector may be substantially proportional to T ₁ T ₂ . The transmittance here is the transmittance from the first input to the first output.

In one embodiment, the transmittance of the beam splitter may be 0.3 to 0.7.

In one embodiment, the squeezed vacuum field generator may include a second harmonic generator that produces a second harmonic of coherent light and an optical parametric amplifier in which the second harmonic is seeded.

In one embodiment, a Stokes pulse generator that generates a Stokes pulse and a dichroic mirror that combines the first output of the beam splitter with the Stokes pulse may be further provided. The first photodetector may measure the pump pulse attenuated by induced Raman scattering (SRS) as a result of irradiating the sample with the output of the dichroic mirror.

The spectroscopic method according to one embodiment includes a step of generating coherent light, a step of generating a squeezed vacuum field, a step of combining coherent light and a squeezed vacuum field by a beam splitter, and a first beam splitter. It comprises a step of balancing the light obtained as a result of the output acting on the sample and the second output of the beam splitter.

(Embodiment)
Hereinafter, the present disclosure will be described with reference to the drawings based on the preferred embodiments. The same or equivalent components, members, and processes shown in the drawings shall be designated by the same reference numerals, and duplicate description thereof will be omitted as appropriate. Further, the embodiment is not limited to the disclosure or the invention, but is an example, and all the features and combinations thereof described in the embodiment are not necessarily essential to the disclosure or the invention.

Below, the quantum enhanced balance detection (QBD) method for ultrasensitive transmission measurement will be described. QBD is an extension of balance detection and can improve the SNR of optical spectroscopy and imaging beyond SQL even when the average power of light is high (> 10 mW).

First, the principle of QBD will be explained, an intuitive diagram of the method and a closed form representation of the SNR will be provided, and the effect of light loss will be explained.

FIG. 1 is a diagram showing an optical measuring device 100 using the principle of QBD. The optical measuring device 100 measures the transmittance of the sample under test (SUT: Sample Under Test) 1.

It includes a beam splitter BS, a first photodiode PD1, a second photodiode PD2, and a processing unit 110.

The coherent light 2 and the squeezed vacuum field 4 are combined by _a beam splitter BS having a transmittance of T1. The transmittance T ₁ of the beam splitter BS is the transmittance from the first input 2 to the first output 6, and T ₁ : (1-T ₁ ) is the split ratio of the beam splitter. The SUT 1 is arranged on the path of one output (first output) 6 of the beam splitter BS, and one of the outputs 6 of the beam splitter BS passes through the SUT ₁ (Sample Under Test) having a transmittance of T2. The transmittance T ₂ of this SUT 1 includes a minute fluctuation ΔT. Although the case of measuring the transmitted light of the SUT1 will be described here, the application of the QBD is not limited to this, and various measurements obtained by the first output 6 of the beam splitter BS acting on the SUT1 are measured. Can be applied to.

The transmitted light 8 of SUT1 is detected by the first photodiode PD1, and the other output 10 of the beam splitter BS is detected by the second photodiode PD2. Instead of the first photodiode PD1 and the second photodiode PD2, a photodetector (photodetector) other than the photodiode (for example, a photoconductive element) may be used.

The processing unit 110 balance _- detects the change amount ΔT of the transmittance T2 of the SUT 1 based on the output of the first photodiode PD1 and the output (photocurrent) of the second photodiode PD2.

For example, the processing unit 110 includes a gain adjusting unit 112 and a difference detecting unit 114. The gain adjusting unit 112 performs appropriate gain control in consideration of the transmittances T ₁ and T ₂ of the beam splitter BS and SUT 1, and weights and adds them. The first amplification unit 112a amplifies the output of the first photodiode PD1 with a _first gain (weighting factor) G1 determined to be substantially proportional to (1-T ₁ ). The second amplification unit 112b amplifies the output of the second photodiode PD2 with a second gain (weighting factor) G ₂ determined to be substantially proportional to T ₁ T ₂ .

The difference detection unit 114 generates a QBD output signal I proportional to the fluctuation ΔT of the transmittance of SUT1 based on the difference between the output of the first amplification unit 112a and the output of the second amplification unit 112b.

The processing in the processing unit 110 may be analog signal processing, digital signal processing, or a combination thereof.

In order to explain the operation of QBD, first consider the case where the squeezed vacuum field is not injected into the beam splitter BS. This is a classical balance detection, in which fluctuations in the intensity of input coherent light cause common mode fluctuations (fluctuations of in-phase components) in the outputs (photocurrents) of the first photodiode PD1 and the second photodiode PD2. Common mode fluctuations can be offset by subtracting the two photocurrents. However, since the beam splitter BS stochastically divides the photons of the coherent light, the shot noise of the photocurrents of the two photodiodes is uncorrelated and cannot be removed by subtraction.

On the other hand, in QBD, a squeezed vacuum field with an appropriately controlled phase is introduced into the beam splitter BS, and two output modes in which shot noise is entangled with each other are generated. By subtracting two optical currents including entangled shot noise by balance detection, shot noise is suppressed, and ultra-sensitive transmission measurement can be realized with an SNR higher than SQL.

The above is the configuration of the optical measuring device 100. Next, the principle of QBD will be described in detail.

The principle of QBD can be intuitively understood by considering the wave functions of the input mode and the output mode of the beam splitter BS. Without loss of generality, it is assumed that the complex amplitude of the coherent light represented by α = x ₀ + ip ₀ is a real number (ie, p ₀ = 0). Also, for the sake of simplicity, it is assumed that T ₂ = 1.

2 (a) and 2 (b) are diagrams showing a two-mode wave function Ψ (x _a , x _b ) at the input and output of the beam splitter BS in the case of balance detection without injecting a squeezed vacuum field.

Consider a two-dimensional wavefunction Ψ (x _a , x _b ). The square of its absolute value | Ψ (x _a , x _b ) | ² gives the probability density. Here, x _a and x _b represent the positions of the harmonic oscillators corresponding to the two modes of input of the beam splitter BS (see Appendix A.1 for details). First, a case without a squeezed vacuum field where coherent light and a (non-squeezed) vacuum field are injected into the beam splitter BS will be described. The wavefunctions of coherent light and vacuum field are Gaussian wavefunctions centered on x0 and ₀ , respectively, and the dispersion is the same (that is, quantum fluctuation). Therefore, the two-mode wave function is a two-dimensional circular Gaussian function centered on (x _a , x _b ) = (x ₀ , 0). (FIG. 2 (a)). At the output of the beam splitter BS, the wavefunction rotates by θ = arccos √ T ₁ in the x _a − x _b plane. (FIG. 2 (b)). The resulting two-dimensional circular Gaussian function can be represented by the product of the wavefunctions x _a and x _b . This indicates that the two modes are separable and there is no correlation between x _a and x _b . Therefore, the fluctuations of x _a and x _b (that is, shot noise) of the two output modes are independent of each other (uncorrelated) and cannot be canceled by balance detection.

3 (a) and 3 (b) are diagrams showing a two-mode wave function Ψ (x _a , x _b ) at the input and output of the beam splitter BS in the case of balance detection in which a squeezed vacuum field is injected.

When a squeezed vacuum field is injected into one of the input ports of the beam splitter BS, the wavefunction of the squeezed vacuum field is compressed along the _xb axis, so the two-mode wavefunction is a two-dimensional elliptical Gaussian function. (Fig. 3 (a)). At the output of the beam splitter BS, the wave function of the two modes rotates by θ (FIG. 3 (b)). x _a and x _b are entangled and cannot be separated into independent wave functions of x _a and x _b (that is, they cannot be represented by the product of the wave functions of x _a and x _b ). Therefore, the shot noises of light at the two output ports of the beam splitter BS are correlated with each other and can be offset by subtraction by balance detection, and the shot noise can be suppressed to less than SQL.

In the description so far, it is assumed that the transmittance T ₂ of the SUT 1 is 1, but a case where an arbitrary transmittance T ₂ <1 can also be described. Therefore, the three-mode wavefunction Ψ (x _a , x _b , x _c ), which is the product of the wavefunctions of the vacuum field introduced by the coherent light, the squeezed vacuum field, and the interaction with SUT1 (here, the loss). think of. x _c represents the position of the harmonic oscillator in the vacuum field introduced by the third mode, the action of SUT1 (here loss).

With x _c , the three-mode wavefunction Ψ (x _a , x _b , x _c ) constitutes a three-dimensional elliptical Gaussian function. The beam splitter BS rotates the ellipse in the x _a -x _b plane, and the loss of SUT1 rotates the ellipse in the x _b -x _c plane. By projecting the probability distribution given by | Ψ (x _a , x _b , x _c ) | ² onto the x _a − x b plane, it is possible to confirm how the loss of _SUT1 affects the SNR.

Quantum mechanical calculation of SNR of QBD is performed to compare the performance of QBD with classical balance detection and amplitude squeeze. Appendix A. By the calculation described in 2, a closed form equation (1) representing SNR is obtained.

　ここで、ｅ^－２ｒ（ｒ≧０）は、スクイーズド真空場のスクイージングレベルを表す。ここで、ＳＮＲは、振幅比ではなく、信号とノイズの間の電力比として定義されていることに注意されたい。αはコヒーレント光の複素振幅であるため、|α|^２は、注目する単一の時間-周波数／空間モードでの光子の数に対応する。

Here, e ^-2r (r ≧ 0) represents the squeezing level of the squeezed vacuum field. Note that SNR is defined here as the power ratio between the signal and the noise, not the amplitude ratio. Since α is the complex amplitude of coherent light, | α | ² corresponds to the number of photons in the single time-frequency / spatial mode of interest.

When the loss of SUT1 is negligible, that is, T2 → 1, the SNR is expressed by the equation ( ₂ ).

The following can be seen from equation (2).
1. 1. First, the SNR can be improved by increasing the squeezing level and is not limited to the transmittance of the beam splitter BS. This is in contrast to the amplitude squeeze based on the displacement of the beam splitter BS. The finite split ratio of the beam splitter BS causes undesired degradation of the squeezed vacuum field, and Appendix A. Limit the achievable squeezing level of 3 (see equation (A32)). In contrast, the QBD detects both outputs of the beam splitter BS, which allows it to overcome the squeezing level limitation of the beam splitter BS and allows the use of a beam splitter BS with a moderate split ratio. ..

2. 2. Second, if | α | ² T ₁ (ie, the optical power passing through SUT 1) is kept constant, the SNR is proportional to (1-T ₁ ). Therefore, the SNR increases as T ₁ decreases. However, at this time, in order to make | α | ² T ₁ constant, it is necessary to increase | α | ² (that is, the optical power of the coherent light source).

Next, how the light loss of SUT1 affects the squeezing level will be described. Although it is not possible in practice, the equation (3) is obtained by taking the limit of r → ∞ in the equation (1).

Equation (3) suggests that the upper limit of SNR does not depend on T ₁ when | α | ² T ₁ is kept constant. Since the SNR depends on (1-T ₁ ) as described above, this is counterintuitive (Equation (2)), but this point can be understood as follows. Since the amount of squeezed vacuum field passing through SUT 1 is also small, the effect of light loss of SUT 1 on the squeezing level becomes smaller as T ₁ increases. As a result, the SNR dependence on T ₁ is corrected, so that the SNR limitation due to the optical loss of SUT 1 does not depend on T ₁ .

(Use)
Subsequently, a method of applying the QBD to an SRS (Stimulated Raman Scattering) microscope will be described. This has recently been considered a powerful method of biological imaging using molecular vibrational contrast [Non-Patent Documents 22-27]. It is known that the SNR of an SRS microscope is limited by shot noise [Non-Patent Documents 22, 23, 28, 29].

Quantum enhancement of SRS microscopes has recently been reported [Non-Patent Documents 13, 15], but it is still difficult to exceed the SNR of classical SRS microscopes. Because the quantum enhancement utilizes a displaced squeezed vacuum field [Non-Patent Document 13] or a seeded OPA [Non-Patent Document 15], the optical power used in the imaging experiment is several milliwatts and the SRS. This is because it is an order of magnitude lower than the typical optical power of a microscope [Non-Patent Documents 24 and 27].

The SRS microscope uses a two-color sync sequence of picosecond pulses called pump pulses and Stokes pulses. Typical wavelengths for pumps and Stokes pulses range from 0.7 μm to 1.1 μm. The Stokes pulse is intensity modulated on the time axis, the pump pulse and the Stokes pulse are combined and focused on the sample. SRS occurs when the molecule in the focal volume has a Raman active oscillation mode and its resonance frequency ω _R matches the frequency difference (ω _p −ω _s ) between the pump pulse and the Stokes pulse. Since the SRS causes the pump pulse to decay and the Stokes pulse to be amplified, the Stokes pulse intensity modulation is transferred to the pump pulse via the SRS. To detect the transferred modulation, the transmitted beam is focused by another objective lens, the pump pulse is extracted by an optical filter and detected by a photodetector. A typical optical power in a photodiode is 10 to 30 mW. The photocurrent in the photodiode contains a transferred intensity modulation component, and the intensity modulation component is locked in by a lock-in amplifier synchronized with the modulation of the Stokes pulse, and an SRS signal is acquired. One-dimensional or two-dimensional imaging is performed by scanning the position of the laser beam or sample.

FIG. 4 is a diagram showing an SRS microscope (also referred to as a QE-SRS microscope) 200 with quantum enhancement. The QE-SRS microscope 200 has a configuration in which a beam splitter BS and a second photodiode PD2 are added to a general SRS microscope 202. In FIG. 4, the scanning mechanism for one-dimensional or two-dimensional imaging is omitted.

The SRS microscope 202 includes a dichroic mirror DM, objective lenses OB1, OB2, a filter F, a first photodiode PD1, and a processing unit 210.

SUT1 is arranged between the pair of objective lenses OB1 and OB2. The pump pulse 12 and the pulse squeezed vacuum field 14 are injected into the beam splitter BS and combined. One of 18 of the two outputs of the beam splitter BS is directly detected by the second photodiode PD2, and the other 16 is guided to the SRS microscope 202.

In the dichroic mirror DM of the SRS microscope 202, the pulse 16 is combined with the Stokes pulse 20, and the combined light 22 is focused on the SUT 1 by the objective lens OB1. From the output light (scattered light of induced Raman scattering) 24 of the SUT 1, the light (that is, the pump pulse) 26 after the Stokes pulse 20 is removed by the filter F is detected by the first photodiode PD1. The combined transmittance of the optical system such as the dichroic mirror DM, the objective lenses OB1 and OB2, and the filter F corresponds to the above _- mentioned transmittance T2. The change in the transmittance of SUT1 due to the induced Raman loss corresponds to the above-mentioned ΔT.

Shot noise can be suppressed by subtracting the outputs (photocurrents) of the two first photodiodes PD1 and the second photodiode PD2 after making appropriate gain adjustments in the processing unit 210. The first amplification unit 212a of the processing unit 210 amplifies the output of the first photodiode PD1 with a _first gain G1 determined to be substantially proportional to (1-T ₁ ). The second amplification unit 212b amplifies the output of the second photodiode PD2 with a second gain G ₂ determined to be substantially proportional to T ₁ T ₂ . The difference detection unit 214 generates a QBD output signal I proportional to the variation ΔT of the transmittance of the SUT 1 based on the difference between the output of the first amplification unit 212a and the output of the second amplification unit 212b.

The lock-in detector 216 also detects the subtracted photocurrent as lock-in. The lock-in detector 216 can obtain an SRS signal with an SNR higher than that of SQL.

The experimental results of the QE-SRS microscope will be explained.

FIG. 5 is a diagram showing the setup of the QE-SRS microscope 300. The QE-SRS microscope 300 includes a pump pulse generator 310, a squeezed vacuum field generator 320, and a Stokes pulse generator 330 in addition to the QBD-SRS microscope 200 of FIG.

The pump pulse generator 310 generates the pump pulse 12. The pump pulse generator 310 includes a titanium sapphire laser 312, a beam splitter BS1, AOM314, and SLM316. The titanium sapphire laser 312 produces a pump pulse. A part of the pump pulse generated by the titanium sapphire laser 312 passes through the beam splitter BS1 and is incident on the AOM314. The AOM314 is provided to adjust the phase of the pump pulse. The SLM316 beam-shapes the output light of the AOM314 and outputs it as a pump pulse 12.

The pump pulse 22 branched by the beam splitter BS1 of the pump pulse generator 310 is input to the squeezed vacuum field generator 320. The mirror M1 guides the pump pulse 22 from the pump pulse generator 310 to the second harmonic generator 322. The second harmonic generator 322 generates the second harmonic 24 of the pump pulse 22.

The OPA324 is a squeezer, and only the pump light of the second harmonic 24 is injected into the OPA324, the seed light of the fundamental wave ω is not injected, and the squeezed vacuum field 14 is generated. The OPA324 is constructed using a single-pass periodic polarization inversion constant ratio composition lithium tantalate (PPSLT: Periodically Poled Stoichiometric LiTaO ₃ ) waveguide.

The Stokes pulse generator 330 includes a Yb fiber laser 332 and a wavelength scanner 334. For hyperspectral SRS measurements, the wavelength of the Stokes pulse 20 is adjustable over a wavelength adjustment range of about 30 nm.

The configuration of the QBD-SRS microscope 200 is as described with reference to FIG. 4, but FIG. 5 shows a part thereof in a simplified manner. A home-made balanced photodetector is used to detect the QE-SRS signal, and a high-frequency spectrum analyzer (RFSA: Radio Frequency Spectrum Analyzer) is included.

Next, the experimental results will be explained.

FIG. 6 is a diagram showing the measurement results of the SRS spectrum of dimethyl sulfoxide-d6 (d-DMSO). FIG. 6 shows (i) when the squeezed vacuum field is not injected, (ii) when the squeezed vacuum field is injected, and when the phase of the pump pulse is optimized, (iii) the squeezed vacuum field is used. The case where the injection is made and the phase of the pump pulse is inappropriate is shown. By injecting a squeezed vacuum field and optimizing the phase of the pump pulse, the noise level can be reduced by 2.06 dB as compared with the case where the squeezed vacuum field is not injected.

FIG. 7 is a diagram showing the evaluation result of squeezing when the sample is not arranged. FIG. 7 shows (i) noise when the squeezed vacuum field is not injected (shot noise), (ii) noise when the squeezed vacuum field is injected (squeezed noise), and (iii) thermal noise. .. During the measurement, it was demonstrated that the squeezed noise was pulsating and the squeezed vacuum field could be generated by changing the frequency ω (phase) of the pump pulse with time by AOM314. It can be seen that the difference between the squeezed noise and the shot noise is larger than 3 dB in the optimum phase state (valley of pulsation), and therefore a squeezing level exceeding 3 dB can be realized.

The squeezing level is mainly limited by the scattering loss when passing through the sample contained in the cuvette.

QBD is advantageous for adopting quantum enhancement in optical measurements using relatively high average power over 10 mW. Previous quantum augmentation spectroscopy used beam splitters with a split ratio of 1-2% [Non-Patent Documents 12, 13], which limits the available optical power of light passing through the sample. rice field. It is possible to use a high power laser source with an average power of several watts to increase the light power through the sample, but such a method is not efficient from a practical point of view. On the other hand, by combining quantum enhancement with QBD, the average power of the light irradiating the sample can be increased while reducing the optical power of the laser light source.

Note that according to equation (2), in balance detection without quantum enhancement, the SNR is lower than in the case without balance detection because the two photodiodes contribute to shot noise. For example, when the beam splitter splits at 50:50, the SNR for balance detection without squeeze is 3 dB lower than with a single photodiode. Therefore, the squeezing level needs to be high enough (<-3 dB) to achieve quantum enhancement. Using a BS with a lower division ratio (eg, 30:70) can increase the SNR to some extent, but because one photodiode PD2 receives stronger light than it passes through the SUT, the photo The diode PD2 may saturate. Saturation can be mitigated by splitting the light into multiples with an additional beam splitter and receiving all output light in parallel with multiple photodiodes.

Some issues remain in applying QBD to SRS microscopes. The most important thing is to realize a high transmittance optical system. This is because the light loss lowers the squeezing level according to equation (1) and sets the upper limit of SNR. Therefore, it is important to use an objective lens with high transmittance [Non-Patent Documents 14 and 15]. In order to achieve high spatial resolution, it is important to magnify the beam at the input of the objective lens, but since a part of the beam is blocked by the pupil of the lens, unnecessary light loss occurs. To avoid this effect, a pair of beam forming optical systems such as Axicon [Non-Patent Document 30] is useful. Further, in order to avoid a decrease in the squeezing level, it is desirable to adopt a photodiode having high quantum efficiency and low thermal noise.

Regarding the pulse squeeze technology, an excellent squeezing level of about -6 dB has been achieved so far by using the single-pass waveguide OPA [Non-Patent Document 31] or the synchronous excitation OPO [Non-Patent Document 32]. In applications to SRS microscopes, waveguide OPA is the first because the bandwidth of the squeezed vacuum field generated by OPA is wider than the bandwidth generated by OPA and can support a sufficient modulation bandwidth for SRS detection. It becomes an option of. Furthermore, the use of waveguide OPA is essential because it can alleviate the strict restrictions on the squeezing level of bulk OPA due to the mode mismatch between the pump mode and the signal mode [Non-Patent Documents 33, 34]. Nevertheless, careful design of the OPA is important for achieving high squeezing levels. [Non-Patent Document 35].

(Modification example)
It will be appreciated by those skilled in the art that the embodiments described above are exemplary and that various modifications are possible for each of these components and combinations of processing processes. Hereinafter, such a modification will be described.

In the above-mentioned SRS microscope, the first photodiode PD1 is used to detect SRS in the traveling direction of the pump pulse, but this is not the case, and backscattered light scattered in the direction opposite to the traveling direction of the pump pulse is emitted. It may be a reflective type to detect.

The application of the optical measuring device according to the embodiment is not limited to the SRS microscope. For example, in the configuration of FIG. 5, SRS spectroscopic measurement may be performed by sweeping the wavelength of the Stokes pulse with the wavelength scanner 334.

In addition to the SRS microscope and SRS spectroscope, the optical measuring device according to the embodiment includes photothermal imaging [Non-Patent Document 38], guided emission microspectroscopy [Non-Patent Document 39], and two-photon absorption microscope [Non-Patent Document 40]. It can be applied to various imaging and spectroscopic measurements including.

It will be appreciated by those skilled in the art that embodiments are exemplary and that there are various variations in each of these components and combinations of processing processes, and that such modifications are also within the scope of the present disclosure or the invention. It is about to be.

(appendix)
A. 1 Wave function in QBD Here, the wave function of the coherent state | α> and the squeezed vacuum field is summarized [Non-Patent Documents 36 and 37]. The position operator x ^ and the momentum operator p ^ satisfy the commutation relation [x ^, p ^] = i / 2, so the momentum operator p ^ is a function of x,
p ^ =-(i / 2) (d / dx)
Suppose it meets.

[a ^, a ^ ^† ] = 1 If you use the annihilation operator a ^ = x ^ + ip and the generation operator a ^ ^† = x ^-ip, the harmonic oscillator corresponding to the time-frequency / spatial mode Hamiltonian
H ^ = h _bar ω (x ^ ² + p ^ ² ) = h _bar ω (a ^ ^† a ^ + 1/2)
It is expressed as. Here, h _bar is the converted Planck's constant, which is the value obtained by dividing the Planck's constant h by 2π. ω is the angular frequency of the light under consideration.

<x | a ^ | 0> = {x-(i / 2) (d / dx) e ^{-x ^ 2} } = 0 and || | 0> || ² = ∫ _－∞ ^∞ | <a | 0> Since | ² dx = 1, the ground state <x | 0> of the harmonic oscillator can be expressed by the following equation.
<x | 0> = (2 / π) ^1/4 e ^{-x ^ 2}

The n-photon state is expressed by the following equation.
| n> = (n!) ^-1/2 (a ^† ) ⁿ | a>

　ここで、D^(α)は変位演算子である。ここでは、x表記の変位演算子D^(x₀)を用い、これにより波動関数をx₀で表すことができる。 Assuming that the complex amplitude α = x ₀ + ip ₀ of coherent light is a real number (that is, p ₀ = 0), the wave function Ψ _α (x) is expressed by the following equation.

Here, D ^ (α) is a displacement operator. Here, the displacement operator D ^ (x ₀ ) in x notation is used, so that the wave function can be expressed by x ₀ .

In the Schrodinger picture, the wavefunction of coherent light changes over time, known as the Gaussian wave packet, which oscillates at the angular frequency ω and has an amplitude of | α |.

The wave function Ψ _s (x) of the squeezed vacuum field is expressed by the following equation. S ^ (r) is a squeezing operator that reduces the wavefunction by an e ^-r times.

This is understood from the fact that the following equation (A4) is taken into consideration, and that the function e ^{r / 2} φ (er x) obtained by scaling an arbitrary function φ (x) satisfies the equation (A5).

In QBD, the quantum states of the two input modes of the beam splitter are considered by the wave function Ψ (x _a , x _b ). Here, x _a and x _b represent the positions of the harmonic oscillators corresponding to the two modes (indicated by a and b). Expressing the coherent state of mode a as ψ _a (x _a ) and the squeezed state of mode b as ψ _b (x _b ), the quantum states of the two modes are ψ _a (x _a ) and ψ _b (x _b ). ) Is given by the tensor product, which is the product of two wavefunctions.

　ここで、ビームスプリッタの透過率はcos²θである。H^_BSはビームスプリッタのハミルトニアンであり、以下のように定義される。これは、角運動量やストークスパラメータS₃と同じ形を有する。

The action of the beam splitter can be expressed using the unitary operator as follows.

Here, the transmittance of the beam splitter is cos ² θ. H ^ _BS is the Hamiltonian of the beam splitter and is defined as follows. It has the same shape as the angular momentum and the Stokes parameter S ₃ .

　ここで、項-2i(x_a^ p_b^ - p_a^ x_b^)は、式（Ａ７）の指数関数に現れるものと同じである。 Therefore, U (θ) Ψ (x _a , x _b ) rotates Ψ (x _a , x _b ) because U (θ) gives a phase shift according to the angular momentum defined as the phase shift due to rotation. It becomes a thing. Alternatively, the rotation of the wave function can be obtained by calculating the following equation.

Here, the term -2i (x _a ^ p _b ^ --p _a ^ x _b ^) is the same as that appearing in the exponential function of equation (A7).

A. 2 Calculation of SNR in the QBD method The SNR of the QBD method is derived using the Heisenberg picture. Here, the creation and annihilation operators change with beam splitters, squeezing and loss. The coherent light, the vacuum field to be squeezed, and the vacuum field annihilation operator introduced by the loss of SUT are written as a ₁ ^, b ₁ ^, and c ₁ ^, respectively.

The squeezed vacuum field annihilation operator b ₂ ^ is given by squeezing the real part of b ₁ ^ with e ^-r and anti-squeezing the imaginary part with ^er .

　ＳＵＴの損失は、入射する光に真空場を結合するから、ＳＵＴの出力光の消滅演算子は、以下の式で与えられる。

After the light has passed through the beam splitter, the output mode annihilation operator is given by the following equation.

Since the loss of the SUT couples a vacuum field to the incident light, the annihilation operator of the output light of the SUT is given by the following equation.

　ここでは、ΔTが非常に小さいため、I^のノイズへの影響は無視できると仮定する。I^のノイズを計算するには、次のようにI^にΔT= 0を代入してI₀^を導出すればよい。

Considering that the photodetector detects the number of photons of the incident light, the operator I ^ of the QBD output is obtained as follows.

Here, it is assumed that the effect of I ^ on noise is negligible because ΔT is very small. To calculate the noise of I ^, substitute ΔT = 0 for I ^ to derive I ₀ ^ as follows.

　またコヒーレント光と真空場の干渉、すなわちショットノイズは、以下の式で表される。

Where b ₂ ^ ^† b ₂ ^ corresponds to the number of squeezed photons. This is negligible compared to the number of photons of coherent light used in QBD. c ₁ ^ ^† c ₁ ^ is zero because it is the number of photons in vacuum. b ₂ ^ ^† c ₁ ^ + b ₂ ^ c ₁ ^ ^† also does not contain coherent light and can be ignored. Therefore, the main noise source is the interference between the coherent light and the squeezed vacuum field, which is expressed by the following equation.

The interference between coherent light and the vacuum field, that is, shot noise, is expressed by the following equation.

The expected value of the output of QBD is derived as follows by using I ^ and the initial quantum state | Ψ>.

Since the expected values of I ₁ ^ and I ₂ ^ are zero, the expected values of the variances of I ₁ ^ and I ₂ ^ are given by the following equations, respectively.

Therefore, by defining SNR as SNR = <I ^> ² / (<I ₁ ^> ² + <I ₂ ^> ² ), the above equation (1) is obtained.

A. 3 Calculation of SNR of displaced squeezed vacuum field In order to clarify the advantage of QBD, the SNR in the transmittance measurement using the displaced squeezed vacuum field is derived [Non-Patent Documents 12 and 13]. Here, only one of the photodiode PDs (PD1) in FIG. 1 is used. Using the same annihilation operator as in the previous section, the operator of the output signal of the photodiode PD is expressed as follows.

Then, by substituting ΔT = 0 for I _a ^, I _a0 ^ is obtained by the following equation.

Further, ΔI _a ^, which is a minute change of Ia ^ proportional to ΔT, is obtained by the following equation.

The dominant noise sources of ΔI _a0 ^ are shot noise I _a1 ^, coherent light and squeezed light interference I _a2 ^, and coherent light and vacuum field interference I _a3 ^, which are expressed by the following equations, respectively.

The expected value of the signal is given by the following equation.

The variances of ΔI _a1 ^, ΔI _a2 ^ and ΔI _a3 ^ are given by:

Therefore, the SNR of the displaced squeezed vacuum field is expressed by the following equation.

Taking the limit of T ₂ → 1, the SNR _DSV is given by the following equation.

Since the denominator is 1 when r = 0 (that is, without squeezing) and T ₁ in the limit of r → ∞, the improvement of SNR by squeezing is limited to 1 / T ₁ by the transmittance of the beam splitter. To.

Using equations (1) and (A32), the SNRs of the QBD and the displaced squeezed vacuum field can be compared, specifically their ratios are given by:

　これは、以下の場合に１より大きくなる。

This ratio is given by the following equation in the limit of T ₂ → 1.

This is greater than 1 in the following cases:

These equations show that QBD is advantageous when the squeezing level is higher than the specific value given in equation (A35). Moreover, QBD becomes even more advantageous as T ₁ increases.

The embodiments merely show the principles and applications of the present invention, and many modifications and arrangement changes are permitted in the embodiments without departing from the ideas of the present invention defined in the claims. Will be.

This disclosure can be used for optical measurements such as spectroscopy and imaging.

100 Optical measuring device BS beam splitter PD1 1st photodiode PD2 2nd photodiode 110 Processing unit 112 Gain adjustment unit 114 Difference detection unit 200 QBD-SRS microscope 202 SRS microscope 1 SUT
DM Dichroic Mirror OB1, OB2 Objective Lens F Filter PD1 First Photodiode PD2 Second Photodiode 210 Processing Unit 310 Pump Pulse Generator 312 Titanium Sapphire Laser BS1 Beam Splitter 314 AOM
316 SLM
320 Squeezed Vacuum Field Generator M1 Mirror 322 Second Harmonic Generator 324 OPA
330 Stokes Pulse Generator 332 Yb Fiber Laser 334 Wavelength Scanner

Claims (7)

A light source that produces coherent light and
A squeezed vacuum field generator that creates a squeezed vacuum field, and
A beam splitter that receives the coherent light at the first input and the squeezed vacuum field at the second input.
A first photodetector that measures the light obtained as a result of the first output of the beam splitter acting on the sample.
A second photodetector that measures the second output of the beam splitter,
A processing unit that processes the output of the first photodetector and the output of the second photodetector to acquire the spectral characteristics of the sample, and
An optical measuring device characterized by being provided with. The optical measuring device according to claim 1, wherein the processing unit weights and subtracts the output of the first photodetector and the output of the second photodetector. When the transmittance of the beam splitter is T ₁ and the transmittance of the second output path of the splitter is T ₂ .
The weighting factor for the output of the first photodetector is substantially proportional to (1-T ₁ ).
The optical measuring device according to claim 2, wherein the weighting coefficient for the output of the second photodetector is substantially proportional to T ₁ T ₂ . The optical measuring device according to any one of claims 1 to 3, wherein the beam splitter has a transmittance of 0.3 to 0.7. The squeezed vacuum field generator is
A second harmonic generator that generates the second harmonic of the coherent light, and
An optical parametric amplifier in which the second harmonic is seeded, and
The optical measuring device according to any one of claims 1 to 4, wherein the optical measuring device comprises the above. A Stokes pulse generator that produces Stokes pulses, and
A dichroic mirror that couples the first output of the beam splitter with the Stokes pulse,
Further prepare
13. The optical measuring device according to any one. The steps to generate coherent light and
Steps to create a squeezed vacuum field,
A step of coupling the coherent light and the squeezed vacuum field by a beam splitter,
A step of balancing light obtained as a result of the first output of the beam splitter acting on the sample and the second output of the beam splitter.
A light measurement method comprising.

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