1. INTRODUCTION

The field of quantum metrology takes advantage of non-classical resources to enhance the precision and resolving power of classical measurement techniques beyond the shot noise limit (SNL) [1,2]. In particular, for optical-based sensing, this limit defines the minimum noise floor achievable with classical resources for the sensing configuration under study and can only be surpassed through the use of quantum states of light such as squeezed or entangled states [3,4]. These states allow for a lower noise floor, which makes it possible to detect signals below the SNL, thus increasing the resolving power of the sensor. This has led to a number of proposals that seek to use these states to enhance classical techniques such as interferometry, spectroscopy, spatial-based measurements, and imaging [5–11].

While the use of quantum states of light to enhance measurements was originally proposed about three decades ago, experimental realizations of quantum-enhanced sensors are only beginning to emerge. Furthermore, the interface between plasmonic sensors and quantum states of light offers a unique opportunity to bring quantum-based sensitivity enhancements to devices that are already used in real-life applications. Due to their robust diagnostic capabilities, plasmonic sensors have found their way into a number of applications such as bio-sensing, atmospheric monitoring, ultrasound diagnostics, and chemical detection [12–18]. In addition, these sensors rely on optical readout techniques and have already been shown to be capable of operating at the SNL when differential detection is used to cancel classical noise sources [19]. Thus, further enhancements for a particular geometry are only possible through the use of quantum states of light.

Here, we demonstrate the ability of quantum states of light to enhance the sensitivity of state-of-the-art plasmonic sensors. While there have been proof-of-principle experimental and theoretical studies of quantum-enhanced plasmonic sensors [20–24], the results presented here represent the first implementation of such a sensor with a sensitivity of the same order of magnitude as the classical state of the art. In particular, we detect changes in the refractive index of air induced by ultrasonic waves. This practical implementation of quantum-enhanced sensing can be easily extended to other measurement configurations and paves the way for real-life applications. More significantly, the level of sensitivity achieved here represents an improvement of nearly 5 orders of magnitude with respect to previous proof-of-principle implementations of quantum-enhanced plasmonic sensors [20–22] and of over 2 orders of magnitude with respect to the classical state-of-the-art ultrasound sensing with plasmonic sensors [17].

We consider surface plasmon resonance (SPR) sensors that consist of an array of sub-wavelength nanostructured holes in a thin silver film. The operation of these sensors is based on the optical excitation of electron oscillations at the interface between a metal and a dielectric, or surface plasmons. This coherent conversion between photons and plasmons gives rise to a transmission through the sub-wavelength holes orders of magnitude greater than the transmission expected from diffraction theory, an effect known as extraordinary optical transmission (EOT) [25,26]. This process preserves the quantum properties of the light [27–30] and makes the use of quantum states of light a viable option to enhance the sensitivity of plasmonic sensors [23,24].

The characteristics of the plasmon resonance are determined by the shape, periodicity, and dimensions of the nano-holes in the array, the thickness of the metal film, and the refractive index of the metal and surrounding dielectric. Thus, SPR sensors exhibit a frequency shift of their resonant response and a corresponding change in optical transmission at a given wavelength as a result of small changes in local refractive index [18], which can be caused by the selective binding of the analyte of interest or a change in pressure.

In general, for EOT sensors, intensity ($I$) measurements are used to estimate the refractive index ($n$). In this case, the sensitivity, or minimum resolvable change in the index of refraction ($\mathrm{\Delta }{n}_{\min }$), is given by

2. EXPERIMENT

In our experiment, we probe the plasmonic sensor with one of the entangled twin beams of light generated via a four-wave mixing (FWM) process based on a double-$\mathrm{\Lambda }$ configuration in hot ${}^{85}\mathrm{R}\mathrm{b}$ atoms [34–36], as shown in Fig. 1. To implement the FWM, a strong pump beam (power of 550 mW and $1/e^2$ waist diameter of 1.0 mm) and a 3.04 GHz frequency downshifted probe beam ($1/e^2$ waist diameter of 0.7 mm) are derived from a Ti:sapphire laser operating at a wavelength of 795 nm. These two orthogonally polarized beams intersect at an angle of 0.5 deg at the center of a 12 mm long ${}^{85}\mathrm{R}\mathrm{b}$ vapor cell heated to 109°C and generate probe and conjugate beams as a result of the FWM process. Conservation of energy requires the simultaneous generation of probe and conjugate. This leads to quantum correlations between the amplitudes of the beams that make it possible to obtain noise levels below the SNL, or squeezing, when performing intensity difference measurements. In particular, with our source we are able to generate twin beams with 9 dB of intensity difference squeezing (equivalent to a noise level 87% below the SNL).

 

Fig. 1. Schematic of the experimental setup. One of the twin beams (probe) generated with a four-wave mixing process is sent through a plasmonic sensor inside a chamber, while the other one (conjugate) acts as a reference for intensity difference noise measurements. The setup is used to detect small changes in the refractive index of air with a sensitivity below the shot noise limit. Inset: double-$\mathrm{\Lambda }$ energy level scheme on which the FWM process is based. BD, beam dump; SA, spectrum analyzer; FG, function generator.

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The plasmonic structure that serves as the sensor consists of an array of isosceles triangular sub-wavelength nanoholes (base of 230 nm, side of 320 nm, and pitch of 400 nm), as shown in Figs. 2(a) and 2(b), patterned by electron beam lithography in a 100 nm thick Ag film evaporated on a boro-aluminosilicate glass substrate with a 70 nm thick indium tin oxide coating. The plasmonic structure has an overall size of $200\mathrm{\mu m}\times 200\mathrm{\mu m}$, and the nano-holes are arranged in a square grid. This configuration leads to EOT of $\sim 66\%$ at the probing wavelength of 795 nm, as shown in Fig. 2(c), consistent with COMSOL finite element numerical modeling [30]. A 200 nm thick layer of poly (methyl methacrylate) (PMMA) is deposited on top of the plasmonic structure to protect the Ag from oxidizing. We have verified that this layer of PMMA does not significantly affect the functionality or sensitivity of the sensor for the ultrasound-based measurements described here. The probe beam is focused to a waist diameter $<20\mathrm{\mu m}$ into the plasmonic structure to avoid beam diffraction from the edges of the sensor. Given that the plasmonic structures are polarization dependent, a $\lambda /2$-wave plate is placed before the sensor in the experimental setup, as shown in Fig. 1, to maximize the transmission.

 

Fig. 2. Plasmonic structure used as sensor. (a) and (b) are scanning electron microscope images of the triangular nano-hole array used as the plasmonic sensor. (c) Transmission spectrum of the plasmonic structure measured with a white light source. At the probing wavelength of 795 nm, the EOT is $\sim 66\%$.

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After the FWM process, the probe beam is used for probing the plasmonic sensor, while the conjugate beam acts as a reference for an intensity-difference measurement. Probe and conjugate beams are detected by two independent photodetectors, and the resulting signals are subtracted with a hybrid junction. The power spectrum of the difference signal is then measured with a spectrum analyzer. The power of the probe beam after the plasmonic sensor is stabilized and kept at 70 μW for all the measurements to avoid saturation of the photodetectors.

To study the response of the plasmonic sensor to changes in the index of refraction of the air, the plasmonic structure is placed inside a hermetically sealed chamber that provides a well-controlled and stable environment. An ultrasonic transducer is used to introduce pressure waves inside the chamber that lead to a modulation of the index of refraction of the air around the sensor at the driving frequency of the transducer. Alternatively, it would also be possible to modulate the intensity of the beam used to probe the sensor instead of modulating the index of refraction to characterize the sensitivity. However, modulating the index of refraction enables a direct measure of the sensitivity by determining the minimum index of refraction modulation level at which the measured signal can be distinguished from the noise.

In order to obtain a measure of the sensitivity, it is necessary to calibrate the change in the index of refraction of the air that is induced by the ultrasonic transducer. The average modulation amplitude of the refractive index ($\mathrm{\Delta }n$) along the path of the probe beam inside the chamber as a function of the driving voltage of the transducer is calibrated by placing the chamber in one of the arms of a Mach–Zehnder interferometer (see Supplement 1).

To compensate for the losses introduced by the plasmonic structure and other optical elements on the probe, the photodetector for the conjugate has an adjustable electronic gain that allows us to obtain the largest possible noise reduction when performing the differential measurements. For our current configuration, the squeezing level of 9 dB initially present in the twin beams is reduced to 4 dB (60% below the SNL) after probing the plasmonic sensor and optimizing the electronic gain.

In general, the SNL refers to the classical noise limit of the optical readout for a sensor in a specific configuration. Thus, when comparing sensors that use quantum noise reduction to those operating at the classical noise limit, identical configurations must be used for the measurements with the quantum states of light and when calibrating the SNL. A measure of the SNL for our sensing configuration is obtained by considering the corresponding classical configuration in which the same detection optimized for the twin beams is used, but with classical coherent states of the same power as the probe and the conjugate.

3. RESULTS AND DISCUSSION

When the ultrasonic transducer is driven at its resonant frequency of 199 kHz, the resulting modulation in the index of refraction leads to a modulation in the transmission of the probe beam through the sensor. Figure 3 shows the measured power spectrum of this signal normalized to the SNL. As can be seen in Fig. 3(a), for a modulation of $\mathrm{\Delta }n=1.6\times {10}^{-7}$ refractive index unit (RIU), the signal is resolved with both coherent states and twin beams. However, an enhancement in the signal-to-noise ratio (SNR) is obtained with the twin beams due to the 4 dB reduction in noise. This makes it possible to resolve smaller modulations, as can be seen in Fig. 3(b), where a modulation of $\mathrm{\Delta }n=8.2\times {10}^{-9}$ RIU is resolvable only with the twin beams.

 

Fig. 3. Enhancement of SNR with twin beams. (a) Measured power spectra when probing the sensor with coherent states, trace (i), and with twin beams, trace (ii), for a modulation of the air refractive index of $1.6\times {10}^{-7}\mathrm{RIU}$. (b) Measured power spectra when the modulation is reduced to $8.2\times {10}^{-9}$ RIU. In this case, the signal is hidden in the noise when probing with coherent states, trace (i), while it can be resolved when probing with the twin beams, trace (ii). Settings for the spectrum analyzer: resolution bandwidth (RBW) = 10 Hz, video bandwidth (VBW) = 1 Hz, center frequency = 199 kHz, span = 2 kHz. All traces are averaged 50 times.

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To obtain a measure of the sensitivity of the plasmonic sensor and the enhancement when using quantum states of light, we perform measurements in which the driving voltage of the ultrasonic transducer is linearly ramped as a function of time. Figure 4(a) shows the measured signal at the driving frequency of the transducer for both coherent states and twin beams. As the driving voltage decreases, the modulation signal decreases until it reaches the noise floor (horizontal traces). At this point it is no longer possible to detect the modulation in the index of refraction as the measured signal is dominated by noise. The noise floor is determined by the noise of the optical field used to probe the sensor and is obtained by turning off the refractive index modulation. As can be seen, the noise starts to dominate the measured signal for a lower value of $\mathrm{\Delta }n$ when probing the sensor with the twin beams. An accurate measure of $\mathrm{\Delta }{n}_{\min }$ for each case is obtained by using the data in Fig. 4(a) to calculate the SNR, shown in Fig. 4(b), and determining the 99% confidence level at which we can distinguish the signal from the noise (see Supplement 1). Taking the detection bandwidth of 100 Hz into account, which is set by the resolution bandwidth (RBW) of the spectrum analyzer, the sensitivity when probing with coherent states is $\sim 8.6\times {10}^{-10}\mathrm{RIU}/\sqrt{\mathrm{Hz}}$, while this value is reduced to $\sim 5.5\times {10}^{-10}\mathrm{RIU}/\sqrt{\mathrm{Hz}}$ when probing with the twin beams. This translates to a measured 56% quantum enhancement, consistent with the theoretically expected 58% quantum enhancement when probing the plasmonic sensor with the measured 4 dB of squeezing (see Supplement 1).

 

Fig. 4. Sensitivity enhancement of plasmonic sensor with quantum resources. (a) Measured signal while linearly ramping the driving voltage of the ultrasonic transducer, i.e., increasing the change of refractive index of air ($\mathrm{\Delta }n$), when probing with coherent states, trace (i), and with twin beams, trace (ii). The baseline noise for both cases is given by the horizontal traces and was measured by turning off the modulation. All traces are averaged 50 times. Settings for the spectrum analyzer: RBW=100 Hz, VBW=10 Hz, zero span, center frequency = 199 kHz, and sweep time = 10 s. (b) Comparison of the SNR when probing the plasmonic sensor with coherent states, trace (i), and with twin beams, trace (ii). A linear fit is used for the calculated SNR. A 99% confidence bound is used to determine when the signal can be distinguished from the noise and to estimate $\mathrm{\Delta }{n}_{\min }$. (c) Comparison with the optimal classical single coherent-state configuration. SNR when probing with twin beams, trace (ii), and with a balanced configuration with two coherent states, each with the same power as the probe, trace (i). Trace (iii) gives the estimated SNR for the single coherent-state configuration.

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The quantum-based sensitivity enhancement is mainly limited by the losses after the FWM process since the level of squeezing is degraded by such losses. In our experiment, the major sources of loss are due to an imperfect EOT through the plasmonic sensor ($\sim 34\%$ loss) and optical losses in the system ($\sim 27\%$ loss), both of which can be minimized. The losses in a plasmonic structure can be reduced by optimizing the design and fabrication process. Since the thickness of the metallic film (100 nm) is much smaller than the plasmon propagation length, in principle it is possible to obtain EOT approaching 100% [37,38]. Minimizing the losses in the system would allow us to take better advantage of the 9 dB of squeezing generated by the source, which could result in a quantum enhancement as large as 182% with respect to the corresponding classical configuration (see Supplement 1). It is worth noting that, as given by Eq. (1), there will be a trade-off between operating at the maximum transmission to obtain the largest enhancement from the squeezed light and in a region of the transmission spectrum where the slope is maximum to obtain the largest possible signal.

It is worth noting that the sensitivities we were able to obtain here are truly state of the art compared with all known classical and quantum plasmonic sensors [19–21]. When compared with previous work on quantum-enhanced plasmonic sensors, our results represent an increase in sensitivity of nearly 5 orders of magnitude. In Ref. [21], the smallest detectable change of refractive index using quantum resources was 0.001 RIU for a bandwidth of 1 kHz, equivalent to $\sim 3\times {10}^{-5}\mathrm{RIU}/\sqrt{\mathrm{Hz}}$, while in Ref. [20] the smallest detectable change of refractive index was 0.014 RIU with each pixel of their spectra acquired in a 400 s period, which corresponds to a sensitivity of $\sim 0.28\mathrm{RIU}/\sqrt{\mathrm{Hz}}$. Moreover, this sensitivity is comparable to the best previously reported classical sensitivity of the order of ${10}^{-10}\mathrm{RIU}/\sqrt{\mathrm{Hz}}$ [19], where optical powers 14 times larger than those we consider were used to improve the limits of detection at the expense of potential thermoplasmonic effects.

If we consider the resources used to estimate $\mathrm{\Delta }{n}_{\min }$ to be the number of photons probing the sensor, then a better classical strategy would be to use a single coherent-state beam. While in practice it is hard to eliminate all the technical noise from a beam of light, it is still useful to compare to the single-beam strategy. To do so we perform a balanced measurement with two coherent states, each with a power equal to the probe beam. In this case, $\mathrm{\Delta }{n}_{\min }=9.6\times {10}^{-10}\mathrm{RIU}/\sqrt{\mathrm{Hz}}$, as shown by trace (i) in Fig. 4(c). We then estimate the single coherent-state sensitivity by taking into account the fact that the balanced coherent-state configuration has a noise floor that is twice as large as a single coherent-state configuration. This leads to trace (iii) in Fig. 4(c), which allows us to estimate $\mathrm{\Delta }{n}_{\min }=6.8\times {10}^{-10}\mathrm{RIU}/\sqrt{\mathrm{Hz}}$ with a single coherent state of the same power as the probe beam, consistent with the order of magnitude estimation for our structure when considering the single beam strategy (see Supplement 1). Thus, even when compared with the optimal classical configuration, the sensitivity is enhanced by 24% through the use of the twin beams.

Although in the current measurement configuration we are detecting refractive index changes induced by ultrasound waves at 199 kHz, the resulting enhancements can be extended to other sensing applications of plasmonic sensors. In general, plasmonic sensors are used to detect DC changes in the index of refraction, where technical noise makes it difficult to generate squeezed light [39,40]. It is possible, however, to perform measurements away from DC by modulating the beam used to probe the plasmonic sensor. This allows the measurement frequency to be shifted to a region where it is possible to take advantage of the squeezed light. Such a technique is routinely used in classical sensing to avoid low-frequency technical noise. This approach would make it possible to extend to quantum enhancement to measure DC changes in the refractive index of the same order of magnitude as the ones presented here.

4. CONCLUSION

In conclusion, we have shown that the use of quantum states of light can improve the detection limits of SPR sensors beyond the SNL. We have demonstrated a refractive index sensitivity comparable to the state-of-the-art classical plasmonic sensors with 14 times less optical power and 5 orders of magnitude higher than previous proof-of-principle quantum-enhanced plasmonic sensors. When probing the sensor with entangled twin beams, an enhancement of 56% is obtained with respect to the corresponding classical configuration. Even when compared with an optimal single coherent-state configuration, which is hard to achieve experimentally due to classical technical noise, a 24% enhancement is obtained. Such a quantum enhancement allows for sensitivities below the classical SNL. Given that quantum-enhanced plasmonic sensors, in general, make it possible to detect smaller changes in the surrounding index of refraction, the results presented here pave the way for further improvements in sensing limits for high precision biomedical and biochemical detection schemes.