🔬 condensed matter

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

This paper proposes and analyzes a scheme to generate squeezed optical states by storing a classical probe pulse in a Bose-Einstein condensate, where collisional interactions induce spin squeezing in the atomic ensemble that is subsequently mapped back onto the retrieved light with predicted efficiencies of several decibels.

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

Published 2026-07-07

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CC BY 4.0

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

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Idea: Turning a "Memory" into a "Squeezing Machine"

Imagine you have a special kind of light memory (like a hard drive for light) made of a cloud of super-cold atoms. Usually, scientists use this memory just to store a light pulse and play it back later, like pausing a video.

This paper proposes a new trick: instead of just storing the light, they use the time the light is "paused" inside the atoms to change the nature of the light itself. Specifically, they turn "normal" light into "squeezed" light.

Think of "squeezed" light as a super-precise tool. Normal light has a bit of "fuzziness" or static noise (like the grain in an old photo). Squeezed light has that noise pushed down in one specific direction, making it incredibly sharp and precise for measurements.

How It Works: The Three-Step Dance

The process involves three main steps, which the authors describe using a "Λ-type" (Lambda-shaped) setup. Here is the breakdown:

1. The Write-In: Stopping the Light

The Setup: You have a cloud of atoms (a Bose-Einstein Condensate, or BEC) that acts like a frozen, super-cooperative crowd.
The Action: You shine a weak laser pulse (the "probe") into this cloud while shining a strong control laser.
The Analogy: Imagine a marching band (the light pulse) trying to walk through a crowded room. The control laser acts like a bouncer who tells the crowd to freeze and hold hands. The band stops moving, but their "formation" (the pattern of the light) is now stored in the way the crowd is holding hands. The light has been converted into a spin wave—a ripple of excitement moving through the atoms.

2. The Storage: The "Twist"

The Action: Once the light is stored, the lasers are turned off. The atoms are left alone for a short time.
The Magic: Even though the light is gone, the atoms are still bumping into each other. Because they are so close and so cold, these collisions act like a giant, invisible hand twisting the formation of the crowd.
The Analogy: Imagine the crowd is holding a long, flexible rope. If everyone just stands still, the rope is straight. But if they start bumping into each other in a specific way, the rope gets twisted and distorted. In physics terms, this is called "One-Axis Twisting."
The Result: This twisting rearranges the "noise" of the system. It takes the random fuzziness and squeezes it down in one direction while letting it expand in another. The atoms are now in a "squeezed" state.

3. The Read-Out: Releasing the Light

The Action: The control laser is turned back on.
The Result: The "bouncer" lets the crowd go, and the stored formation is converted back into a light pulse that flies out.
The Payoff: Because the atoms were twisted while the light was stored, the light that comes out is now squeezed light. It carries the "super-precision" that was built up inside the atoms.

The Challenges: Loss and Noise

The paper is very realistic about what happens in the real world. It's not a perfect vacuum; things get messy.

The "Leaky Bucket": Atoms can get lost (they fly away or get excited by accident). This is like a bucket with a hole in it. As atoms leave, the "squeezing" effect gets weaker.
The "Jitter": When atoms are lost randomly, it adds a little bit of extra shaking (noise) to the system, which fights against the squeezing.
The Sweet Spot: The authors found that there is a perfect amount of time to wait.
- If you wait too short, the atoms haven't twisted enough to squeeze the light.
- If you wait too long, too many atoms are lost, and the noise ruins the squeezing.
- The Finding: They calculated that for their specific setup, waiting about 30 to 35 milliseconds is the sweet spot. At this time, they can get a reduction in noise of about 8 to 10 decibels (a significant improvement in precision).

What They Actually Claim (and What They Don't)

What they claim: They have built a mathematical model that proves this is possible. They show that by storing a light pulse in a specific type of atom cloud, letting the atoms collide, and then reading the light back out, you can generate squeezed light. They predict that under realistic conditions (accounting for atoms getting lost), you can still get several decibels of squeezing.
What they do NOT claim:
- They do not claim to have built a working device in a lab yet (this is a theoretical proposal and simulation).
- They do not claim this will immediately cure diseases or be used in hospitals.
- They do not claim this works for any type of light or any type of atom; it is specific to their proposed setup using Sodium atoms and a specific laser configuration.

Summary

Think of this paper as a recipe for a "precision light generator." Instead of just freezing a light pulse in a block of atoms, the authors suggest using the time the light is frozen to let the atoms "dance" and twist the light's properties. When the light is released, it is sharper and more precise than when it went in, ready to be used for ultra-sensitive measurements.

Technical Summary: Generation of Squeezed Optical States via Stored Classical Pulses in a Bose Gas

Problem and Motivation
The generation of squeezed states is fundamental to quantum technologies, enabling measurement sensitivities beyond the standard quantum limit (SQL) and serving as a resource for quantum information processing. While spin-squeezed states have been realized in atomic platforms via measurement-induced or interaction-driven protocols, and Electromagnetically Induced Transparency (EIT) has enabled long-lived optical storage, a unified scheme that utilizes the storage interval itself to generate squeezing and subsequently maps this non-classicality back to light has been less explored. This work addresses the challenge of generating squeezed optical states by leveraging the nonlinear evolution of a Bose–Einstein condensate (BEC) during the storage of a classical light pulse.

Methodology and Physical System
The authors propose a scheme utilizing a $\Lambda$ -type EIT interface within a two-component BEC (e.g., $^{23}$ Na). The system consists of $N_0$ atoms with two long-lived ground states ( $|1\rangle, |2\rangle$ ) coupled to an excited state $|3\rangle$ .

Write-in Phase: A weak classical probe pulse (mean photon number $\mu_{in}$ ) and a strong control field are applied. Through adiabatic EIT, the probe pulse is mapped onto a collective ground-state spin-wave mode ( $\hat{S}$ ). This process prepares a tunable coherent spin state (CSS) of the two-component BEC. The initial spin orientation (tilt angle $\theta$ and azimuth $\phi_0$ ) is determined by the stored mean excitation number and the phase relation between the probe and control fields.
Storage Phase: The optical fields are turned off, and the system evolves under the effective Hamiltonian of the two-component condensate. In the weak-excitation regime, collisional interactions (s-wave scattering) generate an effective one-axis-twisting (OAT) nonlinearity, $\hat{H}_{OAT} = \hbar\chi \hat{J}_z^2$ . This unitary evolution shears the collective Bloch vector, reducing the variance of one transverse spin component (generating spin squeezing) while increasing the conjugate component.
Readout Phase: The control field is reactivated, converting the collective spin wave back into a propagating optical probe pulse. This readout is modeled as a beam-splitter mapping that transfers the atomic quadrature squeezing to the optical mode.

The theoretical model incorporates realistic constraints, including finite optical depth, spontaneous emission, imperfect mode matching, and irreversible particle losses (one-, two-, and three-body processes). The authors account for loss by evolving mean populations via rate equations and modeling the injection of transverse noise (quantum jumps) as isotropic diffusion in the plane orthogonal to the mean spin.

Key Contributions

Unified Protocol: The paper presents a complete theoretical framework where the EIT memory interface serves not just as a storage device, but as an integral part of the state-preparation mechanism. The "write-store-read" sequence prepares a BEC in a specific CSS, allows collisional interactions to generate squeezing, and maps the result back to a well-defined optical mode.
Analytical and Numerical Modeling: The authors derive exact moments for the OAT dynamics using Heisenberg correlators within a fixed- $J$ Dicke manifold. They extend this to include loss mechanisms by rescaling correlators based on instantaneous populations and adding noise terms derived from stochastic loss rates.
Optical Readout Model: A specific model is developed to map the atomic squeezing parameter ( $v_{A,min}$ ) to the detected optical variance, accounting for readout efficiency ( $\eta_{read}$ ) and the time-dependent degradation of coherence due to loss.

Results
Numerical simulations based on experimentally grounded parameters for a $^{23}$ Na BEC (optical dipole trap, $N_0 = 10^5$ atoms) yield the following findings:

Squeezing Generation: Under realistic conditions, the protocol can generate several decibels of optical squeezing. For an input pulse with $\mu_{in} = 10^3$ , the lossless dynamics predicts a minimum variance of $\approx -10.1$ dB at $t \approx 35$ ms.
Impact of Loss: Including inelastic loss channels (specifically two-body loss in the $|1\rangle-|2\rangle$ channel) degrades the maximum squeezing to $\approx -8.4$ dB and shifts the optimal readout time earlier ( $t \approx 31$ ms). This is due to the competition between interaction-driven correlation buildup and the injection of transverse noise and coherence loss.
Dependence on Input Strength: As the input photon number $\mu_{in}$ increases (from $10^2$ to $2 \times 10^3$ ), the achievable squeezing improves monotonically (reaching $\sim -10$ dB), and the optimal storage time decreases. A larger $\mu_{in}$ creates a larger initial tilt, providing more transverse spin length for the nonlinearity to shear before decoherence dominates.
Mode Matching: The scheme ensures that the retrieved light is in a single, well-defined spatiotemporal mode, determined by the EIT phase-matching conditions, which is crucial for interfacing with quantum networks.

Significance and Claims
The paper claims that this protocol offers a "hybrid route" to generating mode-matched squeezed light. Its primary significance lies in the synchronization of squeezing generation with the memory process: the EIT interface fixes the output mode, while the storage duration controls the accumulated nonlinear evolution, enabling "on-demand" emission of squeezed pulses.

The authors position this approach as compatible with quantum networking and precision measurement, noting that controlled release and mode selectivity are often as critical as the squeezing level itself. They modestly suggest that while current parameters yield several dB of squeezing, the approach could benefit from future improvements in coherence times and loss ratios (e.g., via microgravity platforms or optimized internal states), potentially impacting quantum-enhanced optical interferometry and hybrid atom-light metrology. The work connects early proposals regarding nonlinear effects in stopped light with modern capabilities of high-efficiency, long-lived BEC memories.