Long-Lived Squeezed Ground States in a Quantum Spin Ensemble

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Long-Lived Squeezed Ground States in a Quantum Spin Ensemble

Lin Xin, Maryrose Barrios, Julia T. Cohen, and Michael S. Chapman

Phys. Rev. Lett. 131, 133402 – Published 29 September 2023

Abstract

We generate spin squeezed ground states in an atomic spin-1 Bose-Einstein condensate tuned near the quantum-critical point separating the different spin phases of the interacting ensemble using a novel nonadiabatic technique. In contrast to typical nonequilibrium methods for preparing atomic squeezed states by quenching through a quantum phase transition, squeezed ground states are time stationary with a constant quadrature squeezing angle. A squeezed ground state with 6–8 dB of squeezing and a constant squeezing angle is demonstrated. The long-term evolution of the squeezed ground state is measured and shows gradual decrease in the degree of squeezing over 2 s that is well modeled by a slow tuning of the Hamiltonian due to the loss of atomic density. Interestingly, modeling the gradual decrease does not require additional spin decoherence models despite a loss of 75% of the atoms.

Received 16 March 2022
Accepted 7 September 2023

DOI:https://doi.org/10.1103/PhysRevLett.131.133402

Physics Subject Headings (PhySH)

Quantum control Squeezing of quantum noise

Spinor Bose-Einstein condensates

Atomic, Molecular & Optical

Authors & Affiliations

Lin Xin , Maryrose Barrios, Julia T. Cohen , and Michael S. Chapman^*

School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA

^*mchapman@gatech.edu

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Issue

Vol. 131, Iss. 13 — 29 September 2023

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Images

Figure 1
The spin-1 states in the ${\hat{S}}_{z} = 0$ subspace and their evolution can be visualized on a ${S_{x}, Q_{y z}, Q_{z}}$ Bloch sphere. (a) The initial state is an uncorrelated ground state at $q ≫ q_{c}$ with symmetric uncertainties in $S_{x}$ and $Q_{y z}$ . (b)–(f) Following a sudden quench to $q_{i} ≳ q_{c}$ at $t = 0$ , the ground state remains polar, but the fluctuations evolve periodically along elliptical orbits with a frequency $ω_{i} = 2 π / T$ . (g),(h) A second quench at $T / 4$ to a suitably chosen $q_{f}$ will deexcite the condensate into a stationary squeezed ground state. (i) Standard nonequilibrium method of generating spin-1 squeezing following a sudden deep quench across the QCP to the FM phase [19, 21].
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Figure 2
Time-stationary squeezing and periodic squeezing. (a) Measurement of time-stationary squeezing in the $Δ Q_{y z}$ observable following the double-quench sequence $q_{0} \to q_{i} \to q_{f}$ designed to create a squeezed ground state at $q_{f}$ (blue triangles). Quench 1 is defined as $q_{i} = 1.16 q_{c}$ and $q_{f} = 1.04 q_{c}$ . These data are compared to a single quench $q_{0} \to q_{i}$ (red circles), which exhibit periodic squeezing and unsqueezing in $Δ Q_{y z}$ . Simulation results with $c = - 8.2 \pm 0.1 Hz$ (blue shaded area) are compared with the data. All simulations are scaled $ξ^{2} = (ξ_{sim}^{2})^{0.7}$ to match the observed squeezing. (b) Tomographic measurements of the fluctuations at $t = T / 4$ (red circles) and at a much later time ( $t \sim 3 T / 4$ ) after the second quench (blue triangles). The error bars indicate the standard deviation of measured variance determined from 100 repeated measurements per data point.
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Figure 3
Measurement of $ξ_{S_{x}}^{2}$ versus $t$ following the double-quench sequence for different $q_{f}$ . The solid lines are simulation results, and the shaded regions reflect the sensitivity of the simulations to the uncertainty in $c = - 8.5 \pm 0.1 Hz$ . Quench 1 is the same quench as in Fig. 2. Quenches 2 (purple diamonds) and 3 (green squares) stand for $q_{i} = 1.47 q_{c}$ , $q_{f} = 1.12 q_{c}$ and $q_{i} = 1.06 q_{c}$ , $q_{f} = 1.003 q_{c}$ accordingly. For the quench 3 data, the uncertainty of $c$ may lead to crossing over to the FM phase. Inset: the fidelity of the ground state $F$ determined from the residual oscillation of $ξ_{S_{x}}^{2}$ after the second quench. The maximum fidelity that can be detected (dashed line) is limited by the detection noise.
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Figure 4
Measurement of the long-term evolution of $ξ_{S_{x}}^{2}$ and $ξ_{Q_{y z}}^{2}$ in the squeezed ground state. The solid lines are analytical curves based on Eq. (2) with an evolving critical point $q_{c} (t) = 2 | c (t) |$ due to atom loss $c (t) = c (0) \exp (- 2 t / 5 τ)$ [64]. The blue and red dashed lines are the maximum and minimum variance of the deep-quench squeezed state [21]. The inset shows $Δ S_{x}^{2}$ (red circles), $Δ Q_{y z}^{2}$ (blue squares), and $N$ (green triangles) versus $t$ .
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