Reservoir-Mediated Quantum Correlations in Non-Hermitian Optical System

Recent advances in non-Hermitian physical systems have led to numerous novel optical phenomena and applications. Such systems typically involve gain and loss associated with dissipative coupling to the environment, hence interesting quantum phenomena are often washed out, rendering most realizations classical. Here, in contrast, we propose to employ dissipative coupling to enable quantum correlations. In particular, two distant optical channels are judiciously designed to couple to and exchange information with a common reservoir environment, under an anti-parity-time-symmetric setting of hot but coherent atoms. We realize a non-Hermitian nonlinear phase sensitive parametric process, where atomic motion leads to quantum correlations between two distant light beams in the symmetry-unbroken phase. This Letter starts a new route to exploring the non-Hermitian quantum phenomena by bridging the fields of atomic physics, non-Hermitian optics, quantum information, and reservoir engineering. Potential applications include novel quantum light sources, quantum information processing and sensing, and generalization to correlated many-body systems.

Figure 1

Schematics for observation of quantum correlation in an anti-$\mathcal{P}\mathcal{T}$-symmetry platform. (a) The experiment schematics. Two spatially separated optical channels (Ch1 and Ch2) with orthogonal circular polarizations propagate in the warm paraffin-coated ${}^{87}\mathrm{Rb}$ vapor cell under EIT interaction. The coupling between them is mediated by coherent mixing (through atomic diffusion) of the atomic population and coherence of ground states created in each channel. The cell is mounted inside a four-layer magnetic shielding. Inside the shield a solenoid gives precise control over the internal longitudinal magnetic field. After the cell, the output beams are recollimated and directed to the polarization homodyne detection setup. The noise power of the amplified subtracted photocurrents is recorded with a spectrum analyzer. PBS, polarization beam splitter; BPD, balanced photodetector; -, subtractor; HWP, half-wave plate; QWP, quarter-wave plate. (b) The $\mathrm{\Lambda }$ three-level scheme in the two channels. The ground states are Zeeman sublevels of $|F=2⟩$, and the excited state is $|F=1⟩$ of the ${}^{87}\mathrm{Rb}$ $D1$ line. The left- and right-circularly polarized control fields in Ch1 and Ch2 drive the dipole transitions $|1⟩\to |3⟩$ and $|2⟩\to |3⟩$, with Rabi frequency ${\mathrm{\Omega }}_1$ and ${\mathrm{\Omega }}_2$, respectively. The Zeeman splitting ${\mathrm{\Omega }}_L$ is induced by a common longitudinal magnetic field, serving as either the Larmor frequency in the noise spectra measurement or the two-photon detuning in the EIT measurement [denoted as ${\delta }_B$ as in Fig. 2]. Fictional magnetic fields of opposite sign in Ch1 and Ch2 are, respectively, applied to shift the spin waves frequency by $|{\mathrm{\Delta }}_0|$, via additional off-resonant laser beams (not shown). Phase coherence between the two control fields are not required.

Figure 2

Non-Hermitian parametric interaction between two weak-probe fields aided by anti-$\mathcal{P}\mathcal{T}$-symmetric coupling of spin waves. (a) Probe gain as a function of two-photon detuning ${\delta }_B$, proportional to the common magnetic field applied, under coupled (both channels on) and uncoupled (only one channel on) conditions. Here, “Gain” is defined by the ratio of the probes output power and input power (calibrated at output with a far-off-resonance probe of the same input power) minus one. Positive (negative) value of “Gain” stands for gain (absorption). (b) Gain for the two probes changes as the probe’s phase (in radian) in one of the channels is swept. In (a) and (b), the cell temperature is at $40°\mathrm{C}$. The lines in (b) are to guide the eye.

Figure 3

Discord, EIT separation, and noise spectra at varying $|{\mathrm{\Delta }}_0|$, the frequency offset of both spin waves but towards opposite directions as shown in Fig. 1(b). The left column is experiment and the right is theory result. (a) The discord shown at various $|{\mathrm{\Delta }}_0|$ values. (b) The separately measured EIT peak positions at various $|{\mathrm{\Delta }}_0|$ values. The narrow structure (in dashed box) of the noise spectrum shown in the inset of (a) is displayed in (c)–(f) for sampled $|{\mathrm{\Delta }}_0|$, where the red and blue traces are $\mathrm{Var}({\widehat{X}}_1)$ and $\mathrm{Var}({\widehat{X}}_2)$ respectively, and the green is $\mathrm{Var}({\widehat{X}}_1-{\widehat{X}}_2)$. They are identical to $\mathrm{Var}({\widehat{P}}_1)$, $\mathrm{Var}({\widehat{P}}_2)$, and $\mathrm{Var}({\widehat{P}}_1+{\widehat{P}}_2)$, respectively, which are not shown. The experiment noise spectra (c1)–(f1) correspond to the 1st, 3rd, 7th, and 10th point on the discord curve in (a1). The theory noise spectra (c2)–(f2) correspond to the 1st, 3rd, 7th, and 11th point on the discord curve in (a2). The shot noise level is set at 0 dB in both columns, observed when only one channel is on. As expected, when $|{\mathrm{\Delta }}_0|$ increases, the two spin waves are not synchronized, responsible for decreased contrast of the narrow structure. The discord drop is more dramatic near EP, where the EIT separation curve bends. The slight (abnormal) drop in discord for the left two points in (a1) is due to the unwanted optical pumping of the off-resonant beams which changes $|{\mathrm{\Delta }}_0|$ through ac-stark shift. This optical pumping destroys some coherence and slightly decreases the contrast of the noise spectrum, as can be seen from (c1) compared to (d1). The input power of the control in each channel is $700\mu W$ in the experiment. The cell temperature is at 63°C.