We demonstrate the transduction of macroscopic quantum entanglement by independent, distant plasmonic structures embedded in separate thin silver films. In particular, we show that the plasmon-mediated transmission through each film conserves spatially dependent, entangled quantum images, opening the door for the implementation of parallel quantum protocols, super-resolution imaging, and quantum plasmonic sensing geometries at the nanoscale level. The conservation of quantum information by the transduction process shows that continuous variable multi-mode entanglement is momentarily transferred from entangled beams of light to the space-like separated, completely independent plasmonic structures, thus providing a first important step toward establishing a multichannel quantum network across separate solid-state substrates.
© 2016 Optical Society of America
Plasmonic devices are important for a wide range of applications, from nano-imaging  to subwavelength photonic circuits  to the robust field of surface plasmon resonance (SPR) sensors [3–9]. Recently, several demonstrations have motivated interest in the study of the interaction between quantum states of light and both surface plasmon polaritons and localized surface plasmons (LSPs) [10–18], with the bulk of the work focusing on discrete variables. Aside from quantum plasmonic information processing, the interface of continuous variable (CV) quantum information with plasmons presents an important opportunity for quantum sensing below the photon shot noise limit [19,20]. In particular, it has been shown that the use of CV entanglement beyond simple squeezing in one variable can enhance the sensitivity of quantum sensors even further . Furthermore, establishing entanglement across plasmonic media would facilitate the transfer of quantum information from all-optical networks into solid-state quantum networks, a critical step toward implementing nonlinear plasmonic gates.
In this Letter we outline, to the best of our knowledge, the first demonstration of multi-spatial-mode CV entanglement transduction through independent plasmonic media. This allows us to infer the transfer of entanglement from light to separate and independent plasmons and then back to light, thus providing a first important step toward a CV quantum plasmonic network. Further, through the use of LSPs, which support multiple incident wavevectors , we demonstrate that entangled images can be efficiently transmitted through the plasmonic structures via extraordinary optical transmission (EOT) . These entangled images consist of individual sub-beam areas that are independently entangled with one another , leading to a large number of pairs of plasmon modes across independent media becoming simultaneously entangled with one another during the EOT process. Such entangled states will enable a multichannel plasmonic network for quantum information processing and applications such as super-resolution imaging below the shot noise limit.
LSPs are nonpropagating quantized oscillations of conduction electrons in metallic nanostructures and nanoholes. Through plasmon–plasmon interactions, LSPs on both sides of a thin metal film can couple to each other. This makes it possible to transfer photons to plasmons and back to photons, which enables optical transmission orders of magnitude greater than that expected in diffraction theory, an effect known as EOT. With appropriate design, EOT exceeding 90% is possible .
In order to demonstrate the transduction of entangled images mediated by LSPs, entangled twin beams, or probe and conjugate fields, are generated by four-wave mixing (FWM) in vapor as illustrated schematically in Fig. 1. The nonlinear FWM interaction is based on a double- configuration between the hyperfine ground states and the excited states in at the D1 line (795 nm; see Fig. 1, inset) [24,26,27]. A 750 mW pump beam (“P”) 3 mm in diameter and a 20 μW probe beam (“Pr”) 1 mm in diameter intersect at an angle of 8 mrad in a 12 mm long vapor cell. With this configuration the parametric gain is approximately 4. As a result of the FWM, the probe beam is amplified, and a new field, the conjugate (“C”), is generated in such a way as to conserve energy and momentum. In this process, two pump photons are absorbed and a pair of probe and conjugate photons is generated. The emission of probe and conjugate photons in pairs leads to entanglement between them.
A Ti:sapphire laser tuned 800 MHz to the blue of the , to transition is used to generate the pump. A small portion of the laser beam is split off and frequency shifted with an acousto-optic modulator (AOM) in order to generate the probe. The AOM downshifts the frequency of the laser by 3040 MHz to make it 4 MHz detuned from the two-photon transition to in the ground state. After the AOM, the probe is sent to a digital light processor (DLP) to modify its spatial profile. The DLP is a array of micro-mirrors that can be computer controlled to generate an arbitrary binary image on the input probe to the FWM process. After the DLP, an optical system is used to place the Fourier transform of the image at the center of the Rb cell. This allows us to generate entangled images in which the FWM process copies the image of the probe onto the conjugate field.
Once the entangled images are generated, the probe and conjugate beams are sent to two independent and spatially separated plasmonic structures to study the plasmonic transduction of the quantum and spatial properties of the input optical beams. The plasmonic structures consist of a triangular nanohole array in a silver film 100 nm thick, as shown in the SEM image in Fig. 2(b). The triangles have a base and a height with a pitch of 400 nm. Figure 2(a) shows the transmission spectra of both nanohole arrays normalized to the borosilicate glass substrate transmission obtained with a white light source. The transmission peak at is coincident with the wavelength of our entanglement source, ensuring a strong interaction between the entangled light and LSPs. The transmission of the plasmonic structures was measured to be for the one on the conjugate path and for the one on the probe path. The dotted line in Fig. 2(a) shows the transmission spectrum obtained for the triangular hole array through COMSOL finite element modeling. In order to take some of the limitations of the fabrication process into account, the sharp corners of the triangles have been rounded with a radius of curvature of 15 nm in the modeling. Overall, the modeling agrees well with the measured transmission spectra of both sensors. The reduced overall transmission is a result of the inhomogeneities in the fabricated structures that are not taken into account in the modeling. Figure 2(c) shows the magnitude of the electric field distribution around the triangular nanohole at the air–silver interface for an input electric field polarized along the base of the triangle. As can be seen, the electric field at 795 nm is highly localized to the edges of the structure, which indicates the excitation of LSPs.
We first characterize the effect of the nanostructures on the spatial distribution of the entangled images. Figure 4 shows the input probe image (central figure) of the University of Oklahoma (“OU”) logo generated with the DLP. The top row shows the entangled images that are generated by FWM before the plasmonic structures (no EOT), while the bottom row shows the entangled images after transduction by the plasmonic structures. As can be seen from the images with no EOT, the resolution of the entangled images with respect to the original input probe beam is slightly reduced. This is a result of the limited spatial bandwidth of the FWM process. More importantly, the transduction through the plasmonic structures does not significantly degrade the images, which shows that it preserves the spatial information of the incoming optical field. Overall, these images demonstrate the clear spatial multi-mode nature of both the twin beams and the LSP-mediated EOT process.
CV entanglement in twin beams can be characterized through noise measurements of the real and imaginary parts of the complex electric field. These two variables form a conjugate variable pair and are referred to as the amplitude quadrature () and the phase quadrature (). The variance of these operators for a coherent state, which is the quantum representation of a classical state, corresponds to the standard quantum limit (SQL). The SQL represents a transition between quantum and classical behavior, such that having a state with a noise level in one of its quadratures below the SQL, also known as a squeezed state, is a signature of its quantum nature.
The characterization of CV entanglement requires the measurement of the noise properties of joint quadratures that combine the quadratures of the probe and conjugate. The inseparability condition tells us that two CV systems are entangled if28]. The joint quadratures, and , have been defined such that their SQL is normalized to 1. As a result, the presence of squeezing, or noise levels below the SQL, in both joint quadratures is a signature of the presence of CV entanglement with a larger level of squeezing (lower values of ) indicating a larger degree of entanglement. Thus, the inseparability parameter provides a direct measure of the degree of entanglement present in the system.
The characterization of the inseparability parameter, , can be done through homodyne detection (HD), which allows a direct measurement of the field quadratures. HD requires a local oscillator (LO) beam that serves as a reference for the measurements. The LO is combined with the beam being measured with a 50/50 beam splitter, and the resulting output beams are then sent to a balanced detector. The LO serves two purposes: (1) by changing its phase, it is possible to measure either the amplitude or the phase quadrature of the beam being detected, and (2) the spatial profile of the LO effectively selects out the spatial pattern of the beam being measured. To characterize the CV entanglement properties of the twin beams, we use a double balanced homodyne detection system, with an HD for the probe and another one for the conjugate. The signals from each of the HDs are added and subtracted in order to obtain the sum and difference signals. The noise of the resulting signals is then obtained with an RF spectrum analyzer. By scanning the phase of both LOs in a synchronous way, we can directly measure the joint quadratures needed for the inseparability parameter.
The LOs required to characterize the entangled images are generated by multiplexing the FWM process, such that two spatially separated FWM processes occur inside the same vapor cell, as shown in Fig. 1. This allows us to generate LOs that are well matched to the entangled images that are being characterized. After the vapor cell, the beams that serve as the LOs are sent through an equivalent optical system as the probe and the conjugate with the plasmonic structures replaced by the borosilicate glass substrate. This allows us to obtain a more direct measurement of the effect of the transduction process on the quantum and spatial properties of the entangled images as the measurement apparatus is always the same.
When performing the entanglement measurements, the initial alignment of the HDs is done with the bright entangled images generated by the FWM process; see Fig. 3. This allows us to optimize the mode-matching efficiency (how similar the LO is to the probe or conjugate) of the detection system. We obtain mode-matching of 97% when the entangled images are going through the glass substrate and of 94% when they are going through the plasmonic structures. The fact that the mode-matching does not significantly change with and without the EOT process gives a further indication that LSPs preserve the spatial information of the incoming optical field. After alignment optimization, the input probe beam used to generate the entangled images is blocked and the process grows from spontaneous emission. In this configuration the generated beams are known as vacuum twin beams and the shape of the LOs selects out the spatial profile of the twin beams that is measured.
Figure 4 shows the results of the effect of the plasmonic structures on the CV entanglement of the “OU” images. The images at the center, Fig. 4(b), show the spatial profile of the LOs used for the probe and conjugate HDs. This corresponds to the spatial profile of the vacuum twin beams that is measured by each of the HDs. The blue (red) traces show the noise of the sum (difference) signals normalized to the SQL as the phases of the LOs are scanned linearly in time before, Fig. 4(a), and after, Fig. 4(c), EOT through the plasmonic structures. The minimum of the red and blue trace corresponds to and , respectively, while zero corresponds to the SQL. The noise of both joint quadratures is below the SQL before and after the transduction process, indicating that the CV quantum correlations are preserved by the transfer from photons to plasmons and back to photons. In particular, before the plasmonic structures, both joint quadratures have a noise below the SQL, which corresponds to , while after EOT the noise is below the SQL, which corresponds to . The reduction in the degree of entanglement after EOT is consistent with the reduction that is expected from the losses introduced by the plasmonic structures. Using a beam splitter model to calculate the expected squeezing, we predict 1.15 dB of squeezing after taking the losses due to the plasmonic structures and the slight degradation in HD mode-matching into account.
For the configuration used, the intensity difference squeezing observed for the entangled images with a 20 μW probe input was . The reduction when measuring quadrature squeezing is likely due to the imperfect mode-matching between the LOs and the twin beams.
In conclusion, this experiment demonstrates, to the best of our knowledge, the first transduction of CV entangled quantum images through LSPs. The results obtained show that both the entanglement and spatial properties of the optical beams are preserved by the LSPs and allow us to infer the transfer of entanglement between light and plasmons, providing a first step toward a quantum plasmonic network and pointing to a mechanism for highly parallel quantum plasmonic information processing. In particular, this opens the door for a CV quantum plasmonic entangling gate, which is a major building block in quantum information processing. Further, this paves the way toward ultra-sensitive quantum plasmonic sensors that take advantage of entanglement to enhance signal-to-noise ratios analogous to the techniques pioneered in quantum optics.
W. M. Keck Foundation.
B. L. and R. D. acknowledge support from the Laboratory Directed Research and Development program. This work was performed in part at Oak Ridge National Laboratory, operated by UT-Battelle for the U.S. Department of Energy under contract no. DE-AC05-00OR22725. The nanofabrication and electron microscopy were performed at the Center for Nanophase Materials Sciences, which is a DOE Office of Science User Facility.
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