Generation of squeezed optical states via stored classical pulses in a Bose gas

TL;DR

The paper addresses generating pulsed squeezed optical states using a quantum memory built from a two-component Bose–Einstein condensate. It couples a classical probe into a phase-matched spin-wave via a Λ-EIT interface, prepares a coherent spin state, and leverages collisional interactions during storage to realize one-axis twisting with $H_{\rm OAT}=\hbar\chi\hat{J}_z^2$, producing transverse spin squeezing that is later mapped onto a propagating optical mode upon readout. The authors develop a loss-aware, covariance-based framework that combines exact Heisenberg moments with a reduced-dimension fixed-$J$ approach, incorporating population loss, coherence degradation, and a beam-splitter-like readout with efficiency $\eta_{\rm read}$; they predict several dB of retrievable optical squeezing under realistic sodium parameters and storage times. This memory-synchronized scheme yields mode-matched squeezed light suitable for quantum networking and precision metrology, with the potential for further improvements by extending coherence times and reducing inelastic losses. The work bridges early light-stopping concepts with modern high-efficiency BEC memories to enable programmable squeezed-state generation and retrieval, highlighting practical routes to enhanced quantum-enhanced sensing.

Abstract

We propose and analyze a scheme to generate squeezed light by storing a classical probe pulse in a Bose--Einstein condensate (BEC) and exploiting the nonlinear evolution caused by atom--atom collisions during the storage time. A $Λ$-type optical memory interface maps a chosen temporal probe mode onto a single phase-matched collective spin wave; for a coherent input this prepares a tunable coherent spin state of a two-component BEC, with its initial spin orientation set by the stored mean excitation number and the phase relation between the probe and control fields. Collisional interactions during storage then implement one-axis-twisting dynamics and generate spin squeezing in the atomic ensemble. We account for realistic loss and finite memory and retrieval efficiencies, and model readout as a single-mode beam-splitter mapping that transfers the atomic quadrature squeezing onto a propagating optical mode. We identify optimal storage times and predict that, under realistic conditions, several dB of squeezing can be transferred to the retrieved light.

Figures (3)

• Figure 1: (a) Timing diagram of the $\Lambda$-EIT sequence. A short probe pulse (red) is incident while the control field (blue) is on (write-in). Turning the control off maps the optical excitation onto a collective $\ket{1}\!-\!\ket{2}$ ground-state coherence. After a storage interval with the light fields off, the control is turned back on (read-out) to convert the spin wave back into an emitted probe pulse. Inset: $\Lambda$-level scheme with the probe coupling $\ket{1}\!\leftrightarrow\!\ket{3}$ and the control coupling $\ket{2}\!\leftrightarrow\!\ket{3}$. (b) Illustrative Bloch-sphere representations of the collective pseudospin formed by the two ground states $\ket{1}$ and $\ket{2}$ (south/north poles $\ket{J,-J}\equiv\ket{1}$ and $\ket{J,J}\equiv\ket{2}$). The colored patches schematically indicate the spin-noise distribution on the sphere: starting from a near-isotropic coherent-state spot and evolving into an elliptical distribution during the interaction-only evolution, illustrating the build-up of spin squeezing and the rotation of the principal noise axes.
• Figure 2: (a) Time evolution of the retrieved optical variance $10\log_{10}V_{\mathrm{opt}}(t)$ (blue, left axis) for $\mu_{\mathrm{in}}=10^3$; solid (lossy) and dashed (lossless) curves are shown. The dotted red curve (right axis) shows the total memory efficiency $\eta_{\mathrm{tot}}(t)$ for the lossy case. (b) Best (minimum) retrieved squeezing $\min_t[10\log_{10}V_{\mathrm{opt}}(t)]$ (blue, left axis) and the corresponding optimal time $t^*$ (red, right axis) versus $\mu_{\mathrm{in}}$; the upper axis indicates the equivalent initial spin-tilt angle $\theta$, corresponding to the respective $\mu_{\mathrm{in}}$. Circles: lossy case, squares: lossles case.
• Figure 3: Simulated balanced-homodyne LO-phase scan of the retrieved optical mode at the optimal storage time $t^\ast$. For each $\phi_{\mathrm{LO}}$ we generate $N_{\mathrm{sample}}$ single-shot quadrature outcomes $\epsilon$ by sampling $\epsilon=\mu(\phi_{\mathrm{LO}})+\sqrt{V_{\mathrm{det}}(\phi_{\mathrm{LO}})}\,\xi$ with $\xi\sim\mathcal{N}(0,1)$, where $\mu(\phi_{\mathrm{LO}})=A_{\mathrm{coh}}\cos(\phi_{\mathrm{LO}}-\phi_{\mathrm{coh}})$ and $V_{\mathrm{det}}(\phi_{\mathrm{LO}})=(1-\eta_{\mathrm{read}})+\eta_{\mathrm{read}}\,v_A(\phi_{\mathrm{LO}})$. The heatmaps show $\log_{10}(\mathrm{counts}+1)$ from binned samples: red denotes the lossless reference ($\mathrm{Im}(a_{12})=0$, all loss channels off) and blue (shifted by $\pi/2$ to avoid overlap with the red curve) denotes the lossy $^{23}$Na case (loss channels on; representative $\mathrm{Im}(a_{12})=-0.001\,a_0$ used to set the inter-state two-body loss in the model).