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arXiv:2601.05908 · Physical Review Research

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

Sevilay Sevinçli, Dennis Rätzel, Markus Krutzik, Mehmet Özgür Oktel, Mustafa Gündoğan

quant-phcond-mat.quant-gasSubmitted Jan 9, 2026• Announced Jan 12, 2026• 1 citation
arXivHTMLPDF

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.

Journal reference
Phys. Rev. Research 8, 033016 (2026)
DOI
10.1103/89xy-86yz
Comments
12 pages, 3 figures

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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 ΛΛΛ-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.
This thesis presents a method for generating nonlinear phase shifts on superpositions of photon number states. Light is stored in a Bose-Einstein condensate (BEC) via electromagnetically induced transparency (EIT) memory techniques. Atomic collisions are exploited to generate a nonlinear phase shift of the stored state. The stored light is then revived with the nonlinear phase shift imprinted upon it. We show that this method can be used to develop a nonlinear-sign gate in the regime where the Thomas-Fermi and mean-field approximations are valid. We test these approximations using realistic parameters to find that these approximations pass the standard tests for validity in a single-component condensate. However, for the two-component condensates considered here, we find that these conditions are not sufficiently strict. Therefore, we find a stronger set of conditions and show for the same set of parameters that the approximations are invalid.
We theoretically explore coherent information transfer between ultraslow light pulses and Bose-Einstein condensates (BEC's) and find that storing light pulses in BEC's allows the coherent condensate dynamics to process optical information. We consider BEC's of alkali atoms with a $\ensuremath{\Lambda}$ energy level configuration. In this configuration, one laser (the coupling field) can cause a pulse of a second pulsed laser (the probe field) to propagate with little attenuation (electromagnetically induced transparency) at a very slow group velocity $(\ensuremath{\sim}10\phantom{\rule{0.3em}{0ex}}\mathrm{m}∕\mathrm{s})$ and be spatially compressed to lengths smaller than the BEC. These pulses can be fully stopped and later revived by switching the coupling field off and on. Here we develop a formalism, applicable in both the weak- and strong-probe regimes, to analyze such experiments and establish several results: (1) We show that the switching can be performed on time scales much faster than the adiabatic time scale for electromagnetically induced transparancy even in the strong-probe regime. We also study the behavior of the system changes when this time scale is faster than the excited state lifetime. (2) Stopped light pulses write their phase and amplitude information onto spatially dependent atomic wave functions, resulting in coherent two-component BEC dynamics during long storage times. We investigate examples relevant to 87Rb^{87}\mathrm{Rb}87Rb experimental parameters and see a variety of novel dynamics occur, including interference fringes, gentle breathing excitations, and two-component solitons, depending on the relative scattering lengths of the atomic states used and the probe to coupling intensity ratio. We find that the dynamics when the levels $\ensuremath{\mid}F=1,{M}_{F}=\ensuremath{-}1⟩$ and $\ensuremath{\mid}F=2,{M}_{F}=+1⟩$ are used could be well suited to designing controlled processing of the information input on the probe. (3) Switching the coupling field on after the dynamics writes the evolved BEC wave functions density and phase features onto a revived probe pulse, which then propagates out. We establish equations linking the BEC wave function to the resulting output probe pulses in both the strong- and weak-probe regimes. We then identify sources of deviations from these equations due to absorption and distortion of the pulses. These deviations result in imperfect fidelity of the information transfer from the atoms to the light fields and we calculate this fidelity for Gaussian-shaped features in the BEC wave functions. In the weak-probe case, we find that the fidelity is affected both by absorption of very-small-length-scale features and absorption of features occupying regions near the condensate edge. We discuss how to optimize the fidelity using these considerations. In the strong-probe case, we find that when the oscillator strengths for the two transitions are equal the fidelity is not strongly sensitive to the probe strength, while when they are unequal the fidelity is worse for stronger probes. Applications to distant communication between BEC's, squeezed light generation, and quantum information are anticipated.
We demonstrate experimentally an alternative method for the dynamic generation of atomic spin squeezing, building on the interplay between linear coupling and nonlinear phase evolution. Since the resulting quantum dynamics can be seen as rotation and shear on the generalized Bloch sphere, we call this scheme twist-and-turn. This is closely connected to an underlying instability in the classical limit of this system. The short-time evolution of the quantum state is governed by a fast initial spreading of the quantum uncertainty in one direction, accompanied by squeezing in the orthogonal axis. We find an optimal value of ${\ensuremath{\xi}}_{\mathrm{S}}^{2}=\ensuremath{-}7.1(3)$ dB in a single Bose-Einstein condensate and scalability of the squeezing to more than 104{10}^{4}104 particles with ${\ensuremath{\xi}}_{\mathrm{S}}^{2}=\ensuremath{-}2.8(4)$ dB.
A reversible quantum memory allowing us to store and retrieve quantum information serves as a key necessity for implementing many of novel quantum information protocols. As light serves as a reliable long-range carrier of quantum information, and atoms offer the possibility of long storage times, current attempts at creating quantum memories focus on the transfer of the quantum fluctuations of light onto atomic coherences. The work in this thesis focuses on the development of a quantum memory for squeezed light using an ensemble of cold Cesium atoms stored in a magneto-optical trap. Our two major milestones were the development of a source of nonclassical light, and the development of a suitable atomic medium for storage. We first present the results of our efforts to generate a source of squeezed vacuum states resonant with the Cesium D2 line using a PPKTP nonlinear crystal inside of an optical parametric oscillator. Additionally, we characterize these squeezed states by carrying out a quantum state tomography using an iterative maximum likelihood approach. Next we look at the development of a new experiment which would allow us to use cold Cesium atoms as a storage medium in our recently developed magneto-optical trap. As this requires an array of novel tools and experimental techniques, we will discuss the development of these elements, and how they have furthered our progress towards storing quantum states onto our Cesium atoms, and eventually entangling two atomic ensembles.
We propose a scheme to store the spin-nematic squeezing in a spinor Bose-Einstein condensate by applying periodic microwave pulses. For a proper pulse period and phase shift, the squeezing can be enhanced and maintained for a long time, which realizes the storage of the maximal squeezing. We also propose a method to generate the spin-nematic squeezed vacuum, which is associated with negligible occupation of the squeezed modes, through an adiabatic sweep of the magnetic field. It is shown that the method can be readily implemented for both ferromagnetic and antiferromagnetic condensates.
In this thesis I explore the use of collective spin angular momentum as a platform for quantum information processing. Such systems have several nice features that make them excellent choices for such protocols, especially ones where information is also stored in photonic variables. The longer coherence times of atoms makes it possible to store information from light in atoms for future use, and it is generally easier to couple atomic variables than to create nonlinear interactions of light. Above and beyond the advantages of atomic systems, collective atomic systems have additional strengths. In the limit of a large number of atoms, the collective variables of atomic systems have a natural connection to the bosonic algebra of light (known as the Holstein-Primakoff or HP approximation) where components of the collective spin angular momentum effectively act as quadratures, making them natural systems for coupling to light. Also, collectively addressing the atoms allows one to access a large state space without individual addressing of the atoms. A natural first step towards control of these collective variables is generating large amounts of atomic spin squeezing. In the HP approximation going from rotations to squeezing corresponds to going from linear to quadratic interactions in the atomic quadratures; for extremely large squeezing one should see the breakdown of the HP approximation and the ability to generate arbitrary collective atomic states. I have sought to improve previous schemes for the spin squeezing of atomic ensembles, such as the proposal of Takeuchi et. al. based on coherent quantum feedback. In this scheme a beam of linearly polarized light passes through the atomic ensemble (prepared in a coherent state), coupling to the atoms through a state-dependent index of refraction (the Faraday effect). 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By first measuring one quadrature of the light, and then performing a measurement-dependent rotation on the atomic ensemble, it is possible to decouple the atoms and light so that the loss of the light does not reduce the atomic squeezing. This results in an improvement of the rate of atomic spin squeezing. The nonlinear shearing interaction that remains still falls short of the exponential squeezing seen in optical parametric amplification. The reason for this can be seen by decomposing the shearing interaction into squeezing along a given quadrature followed by a rotation. The rotation leads to a constantly changing axis along which the squeezing occurs, and thus the squeezing builds up more slowly. This can be corrected for by breaking up the light pulse into a sequence of small pulses, and performing a small phase matching rotation after each pulse. The squeezing then adds up along a constant direction, rather than along a constantly varying direction. This results in still further improvement of the rate of atomic spin squeezing. A complete model includes the effects of photon-atom scattering and other noise and loss effects on the overall rate of squeezing. Previous derivations of noise due to photon-atom scattering have started with the unjustified assumptions that the atomic and photonic decoherence channels were both Gaussian and independent of correlations between the two subsystems. They then proceed with very general statistical arguments that rely upon these simplifications. My work begins with the more fundamental master equation picture in which I find the Linblad jump operators. I find that in general the photonic and atomic loss channels are not independent, with the intensity of the light dictating the details of this dependence, and find the conditions under which the Gaussian approximation holds. 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