Quantum-Enhanced continuous-wave stimulated Raman spectroscopy

Stimulated Raman spectroscopy has become a powerful tool to study the spatiodynamics of molecular bonds with high sensitivity, resolution and speed. However, sensitivity and speed of state-of-the-art stimulated Raman spectroscopy are currently limited by the shot-noise of the light beam probing the Raman process. Here, we demonstrate an enhancement of the sensitivity of continuous-wave stimulated Raman spectroscopy by reducing the quantum noise of the probing light below the shot-noise limit by means of amplitude squeezed states of light. Probing polymer samples with Raman shifts around 2950 $cm^{-1}$ with squeezed states, we demonstrate a quantum-enhancement of the stimulated Raman signal-to-noise ratio (SNR) of 3.60 dB relative to the shot-noise limited SNR. Our proof-of-concept demonstration of quantum-enhanced Raman spectroscopy paves the way for a new generation of Raman microscopes, where weak Raman transitions can be imaged without the use of markers or an increase in the total optical power.


I. INTRODUCTION
Optical quantum sensing exploits the unique quantum correlations of non-classical light to enhance the detection of physical parameters beyond classical means [1][2][3][4][5]. While several different quantum states of light can, in principle, be used to provide such a quantum advantage, so far, it is only the ubiquitous squeezed states of light that have demonstrably shown to provide a real practical advantage [6][7][8]. Squeezed states of light have for example enabled quantum-enhanced measurements of mechanical displacements [5,9], magnetic fields [10,11], viscous-elasticity of cells [12] and, most prominently, gravitational waves [13]. Another field that could significantly benefit from quantum-enhanced sensing by means of squeezed light -but yet not demonstrated -is Stimulated Raman Spectroscopy (SRS).
SRS is a very powerful technique to perform real-time vibrational imaging of living cells and organisms and it has therefore provided a deeper understanding of properties of biological systems [14][15][16][17]. It is based on the stimulated excitation of a Raman transition of the sample under interrogation, thereby resulting in a measurable stimulated Raman loss and gain of the two input beams, respectively. It allows for non-invasive and invivo measurements with short acquisition times [18] and has enabled the structural and dynamical imaging of lipids [19,20] as well as the characterization of healthy and tumorous brain tissues [21,22].
In SRS, the sensitivity and the imaging speed are fundamentally limited by the noise level (often shot-noise) of the probing laser [23,24] but can in principle be arbitrarily improved simply by increasing the power of the input beams. However, in biological system, especially in living systems, the power must be kept low to avoid changing the biological dynamics of the specimens or even damaging it due to excessive heating. Leaving the optical power at a constant level, the sensitivity and bandwidth of the SRS can be boosted by reducing the shot-noise level using squeezed states of light.
In this article, we demonstrate the quantum enhancement of continuous-wave (cw) SRS using amplitude squeezed light. We demonstrate its functionality and superiority by spectroscopically measuring the carbonhydrogen (C-H) vibrations of polymethylmethacrylate (PMMA) and polydimethylsiloxane (PDMS) with a sensitivity-improvement of approximately 56% relative to shot-noise limited Raman spectrometer. Our measurement method has the potential to enable new measurement regimes of Raman bio-imaging that are inaccessible by the conventional shot-noise limited Raman spectrometer.

II. BASIC CONCEPT
SRS employs two laser beams -known as the pump and the probe (Stokes) laser beams -to coherently excite a selected molecular vibration of the system under investigation. If the vibrational frequency of the chemical bond matches the frequency difference of the pump and probe laser, the Raman interaction is stimulated and as a result significantly amplified by orders of magnitude. In the stimulated Raman effect, a photon is annihilated from the pump beam and simultaneously a Raman shifted photon is created in the background noise of the probe beam. This background noise is fundamentally limited by shot-noise when using a probe beam in a coherent state from a conventional laser, but it can be reduced by using a laser beam in a squeezed state. By using a bright amplitude squeezed beam (squeezed state with a large coherent excitation), the quantumenhanced sensitivity is directly proportional to the standard deviation of the squeezed amplitude quadrature, ∆X: δ ∝ ∆X/ √ I SRS . Here I SRS is the intensity of the SRS signal which changes linearly with the intensity of the probe (I s ) and pump (I p ) as I SRS = KI p I s , where K is a constant related to the number of probed molecules and their Raman cross section [25]. It is thus clear that the sensitivity can be improved without chang-arXiv:2002.04674v1 [physics.optics] 11 Feb 2020 ing the power by reducing the noise of the amplitude quadrature.

III. EXPERIMENTAL SETUP
The experimental setup is shown in Fig. 1. It consists of two modules: the bright squeezed light module and the SRS module as will now be discussed in detail.
Bright Squeezed Light Module: The laser source was an Innolight GmbH Diabolo operating at 1064 nm with an internal module for second harmonic generation (SHG) at 532 nm. The squeezed state was generated in a linear optical parametric oscillator (OPO) cavity consisting of a periodically poled potassium titanyl phosphate (PP-KTP) crystal and a hemispheric coupling mirror. When pumping with a power of 80 mW at 532 nm, setting the phase of the pump beam to deamplification and injecting a seed beam with a power of 600 µW at 1064 nm, the OPO produced 7 dB of amplitude squeezed light. More details about the squeezed light source can be found in [26]. The amplitude squeezed light and a coherent beam at 1064 nm were combined on an asymmetric (99/1) beam splitter to produce a bright amplitude squeezed beam. The phase between these beams was actively stabilized by feeding a phase shifter in the coherent beam path with an error signal that was generated by electronically demodulating the photo detected beat of the bright coherent beam and the 37.22 MHz phase modulation side-bands accompanying the squeezed field. The output of the 99 % port of the BS was sent to the SRS module serving as the probe beam for Raman spectroscopy.
Stimulated Raman Module: The pump beam for SRS was a tunable Ti:Sapph laser (MSquare SolsTiS) scanned from 800 nm to 830 nm. It delivered a maximum output power of 200 mW which could be adjusted at the entrance to the microscope. The pump beam intensity was modulated at 10.45 MHz with a sinusoidal function using a resonant electro-optical amplitude modulator. The beam size of the pump beam was adjusted with a set of lenses (MM lenses) in order to optimize the overlap with the probe beam. A fine adjustment in the polarization between the pump and the probe beams was made using a HWP (half-wave plate) in the probe path. After combining the probe and the pump beams at a dichroic mirror, both beams were focused to a spot size of 2.5 µm on the sample with a 20x microscope objective. The beams were collected and collimated by a second microscope objective after which the pump beam was filtered using a long-pass filter and the probe beam was detected using a photodiode with a quantum efficiency of more than 99 % (Fermionics InGaAs FD500). The stimulated Raman gain was deduced from the power spectrum which was recorded using an electrical spectrum analyzer.
An important factor when using squeezed light are the optical losses in the optical pathway of the squeezed beam. From the output of the OPO cavity to the en-trance of the microscope we estimated an overall optical efficiency of around η path = 85 %, while each of the two microscope objectives had a transmission efficiency of 97 %. The visibility between the coherent and the squeezed beam was 95 %. Thus, the total efficiency transmission of the 1064 nm path including also the detection losses was estimated to η total =67 %.
In this work we use two different solid samples to characterize the SRS process, PMMA and PDMS. Both samples have Raman transitions in the region between 2800-3100 cm −1 corresponding to vibration modes of C-H bonds [27,28]. We start by classically characterizing the Raman transition of a PMMA sample of 2 mm thickness and a pump laser with a power at the sample of 38 mW and tuned to the wavelength of 810.241 nm to hit the Raman transition at 2948.32 cm −1 . The SRS signal was measured on the probe beam (due to the stimulated gain) at the modulation frequency of the pump at 10.45 MHz, and we acquired a power spectrum around this frequency. In absence of the SRS signal only measurement noise was detected. The data presented have all been measured using a resolution bandwidth of 30 Hz and a video bandwidth of 1 Hz, each data point was averaged 30 times and the electronic noise was subtracted in all the measurements. The probe power was changed from 250 µW to 2.0 mW, as shown in Fig. 2a) and we clearly observe the expected linear dependency between SRS signal and probe power. The polarization behavior between pump and probe beams are shown in Fig. 2b) where the red trace represents the signal when the pump and probe beams were parallel polarized while the blue trace corresponds to the signal when the beams were orthogonal polarized. It is clear that the Raman signal disappears in the latter case, thus further corroborating the presence of real Raman signal in the former case [29,30]. Both traces were normalized by the shot-noise.
Having verified the C-H Raman transition, in the following we present the demonstration of quantumenhanced SRS. To clearly demonstrate quantumimproved performance beyond the conventional approach, we conducted the experiment both with the probe beam in a coherent state (limited by shot-noise and representing the conventional approach) and in the squeezed state. The experimental scheme could easily be swapped between the two modes of operation simply by blocking and unblocking the squeezed vacuum state which will have no effect on the probe or pump input powers. Figure 3 presents our experimental results for quantum-enhanced SRS. We present the spectra for the Raman shift of PMMA using both a coherent state (for comparison) and a squeezed state with optical powers of 1.3 mW while the pump power was set to 24 mW (Fig. 3a) and 11 mW (Fig. 3b)  usage of squeezed light significantly improves the signalto-noise ratio and therefore the sensitivity of the Raman spectrometer. We see in particular that for pump powers lower than around 11 mW, the Raman signal is almost embedded in shot-noise and only becomes pronounced when using squeezed states of light. It is therefore clear that by using the quantum-enhanced operation mode, it is possible to attain Raman signals even for low pump powers. This is of importance when studying fragile biological systems where excessive powers might change the dynamics of the system.

IV. EXPERIMENTAL RESULTS
The SRS process provides a Raman spectrum similar to the spectrum generated using Spontaneous Raman Spectroscopy techniques. Using a PDMS sample and sweeping the pump laser, manually, from 803.36 nm to 816.36 nm, the Raman spectrum of C-H stretching modes in the region between 2850-3100 cm −1 was acquired and it is depicted in Fig. 4. The probe and the pump optical powers were 1.3 mW and 28 mW, respectively. While scanning the wavelength of the pump laser, the optical pump power was continuously measured and used to normalize the acquired Raman spectrum at every wavelength. In Fig. 4 the spectra are shown for coherent (red trace) and squeezed states (blue trace). Lorentzian multi-peak fits were used to obtain the two Raman shifts in table I.
To demonstrate the potential of using the quantumenhanced Raman spectrometer as a microscope, we performed a rough raster scan of a sample consisting of three different polymers; PMMA, PDMS and polystyrene. A 3-axes translational stage with differential micrometer screws was used to move, manually, the sample position in steps of 1 mm in a square region of 7x7 mm 2 . The SRS signal was acquired using coherent and squeezed states of light alternately for each displacement. Ap-plying an average pump power of 28 mW and a probe power of 1.3 mW, the pump laser wavelength is set up to 810.213 nm corresponding to a Raman shift 2948.75 cm −1 and the PMMA content in the sample was detected. Fig. 5 a) shows the result. Afterwards, to detect the PDMS content in the sample, the pump wavelength was changed to 813.111 nm corresponding to the vibrational mode 2904.76 cm −1 . The result is shown in Fig. 5 b). The remaining area comprising polystyrene exhibits no signals as it has no vibrational modes in the interrogated frequency region. We clearly see from the figure that PMMA and PDMS can be distinguished with the method, and we also find that squeezed light outperforms coherent light operation in the entire imaging plane. These proof-of-concept imaging measurements demonstrate the usefulness of the quantum-enhanced Raman method for microscopy.

V. CONCLUSION
In summary, we demonstrated a sensitivity enhancement of the stimulated Raman process using squeezed states of light. The quantum enhancement was measured to be more than 50% in comparison to the conventional approach with coherent states. Our technique was used to visualize spectroscopically the Raman bands within the C-H stretching region of polymer samples (PMMA and PDMS) and to perform chemically specific imaging measurements. The sensitivity of our quantum spectrometer can be further improved by minimizing the optical losses of the system and by employing states with a higher degrees of squeezing. Moreover, to realize real and highresolution SRS imaging, the sample should be scanned   with high spatial resolution and the objectives replaced with ones with higher numerical apertures. We believe that our demonstration opens the door to new possibilities for Raman spectroscopy and microscopy. Using squeezed light to enhance the sensitivity of the stimulated Raman signal enables studies of biological samples with a lower risk of damage due to high beam powers. This might enable the studies of bio-physical effects that may not be visible using the standard classical approaches. The presented method is not limited to the wavenumber range investigated in this work but can be extended to the fingerprint region (500-1800 cm −1 ) by appropriate choice of laser wavelengths, thereby giving The EMPIR initiative is funded by the European Union Horizon 2020 research and innovation program and cofinanced by the EMPIR participating states.

Disclosures
The authors declare no conflicts of interest.