Optimizing decoherence in the generation of optical Schrödinger cat states

TL;DR

This work tackles decoherence in generating optical Schrödinger cat states by leveraging cavity Rydberg EIT, which allows parity-dependent photon reflection with tunable loss channels. The authors develop a detailed loss model, distinguishing loss during generation from post-generation loss, and show how to minimize decoherence by tuning the cooperativity and blockade parameters, particularly achieving $\Lambda_{\downarrow} \approx C$. Their analysis predicts that mean photon numbers around $\alpha_{\text{out}}^2 \sim 28$ (roughly $30$) are feasible with existing technology, while maintaining sizable cat visibility. The key contribution is identifying a regime where photon loss does not heavily decohere the cat state, enabling practical optical cat-state generation for quantum information tasks. This has significant implications for scalable quantum optics experiments and photonic quantum information processing.

Abstract

We propose to use cavity Rydberg electromagnetically induced transparency to generate Schrödinger cat states of optical photons. We predict that this should make it possible to generate states with relatively large mean photon numbers. With existing technology, mean photon numbers around 30 seem feasible. The main limitation is photon loss during the process, which generates the state. The ability to tune the strength of the photon loss caused by atomic spontaneous emission makes it possible to have little decoherence despite significant photon loss during the generation of the state.

Figures (4)

• Figure 1: (a) Scheme of a cavity Rydberg EIT setup. Signal light coming from the left impinges on the cavity I/O coupler. This light can be reflected or enter the cavity, in which it interacts with an atomic ensemble. Light can leave the cavity through the I/O coupler, thus staying in the useful beam path, or it can leave the cavity into the environment. The latter happens because of atomic spontaneous emission or imperfections of the HR mirror(s). (b) Atomic energy level scheme. EIT signal light (red) and coupling light (blue) is resonant with the atomic transition $|g\rangle \leftrightarrow |e\rangle$ and $|e\rangle \leftrightarrow |r\rangle$, respectively. There is an additional Rydberg state $|r'\rangle$, which may carry a stationary excitation, which is not coupled to the light but, if populated, will give rise to Rydberg blockade.
• Figure 2: (a) Loss coefficients describing the reduction of the cat visibility as a function of the parameter $\Lambda_{\downarrow}$ for $1-\eta_\text{esc}= 1.75\%$ and $C= 21$. $\Lambda_{\downarrow}$ is in essence the Rabi frequency of the EIT coupling light. $L_a$ (blue line) of Eq. \ref{['La']} represents spontaneous emission by the atomic ensemble. $L_m$ (orange line) of Eq. \ref{['Lm']} represents loss from the highly reflective mirrors. $L_\text{gen}$ (green line) of Eq. \ref{['L-gen-C-Lambda']} represents the reduced cat visibility $V_\text{out}$ according to Eq. \ref{['V-out-L-gen']}. $L_\text{gen}$ is the relevant figure of merit. This is minimized at $\Lambda_{\downarrow}= C$ (dashed vertical line) because $L_a$ vanishes here, while $L_\text{cav}$ and $L_m$ vary slowly as a function of $\Lambda_{\downarrow}$ near $\Lambda_{\downarrow}= C$. (b) Amplitude of the spontaneously emitted light $a_{{\uparrow}/{\downarrow}}$ divided by the amplitude impinging on the cavity $\alpha_\text{in}$. The vanishing of $L_a$ (see part a) at $\Lambda_{\downarrow}= C$ is caused by the fact that here $a_{\uparrow}= a_{\downarrow}$. Here, spontaneously emitted light does not carry any information about the qubit state into the environment. This is why it is advantageous to work at $\Lambda_{\downarrow} = C$.
• Figure 3: The real number $V_{ij}$ of Eqs. \ref{['S-ij-beta-ij-V-ij']} and \ref{['V-ij-Bessel']}, which characterizes the overlap of the modes of the far-field electric-dipole radiation emitted by two atoms, as a function of the scaled distance between the atoms $kr_{ij}$. Different colors represent different values of the scalar product of the complex polarization unit vector $\bm \epsilon$ and the unit vector of the interatomic distance $\bm e_{ij}$. For small (large) $kr_{ij}$, the two modes are almost identical (orthogonal).
• Figure 4: Monte-Carlo results for the dependence of $\overline{B_{{\uparrow}{\downarrow}}}$ of Eq. \ref{['B-up-dn-def']} on $N_a$. The line shows a fit of the power-law function \ref{['B-up-dn-power-law']} to the numerical results (circles).