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arXiv:2310.15473 · Physical Review A

O(1) benchmarking of precise rotation in a spin-squeezed Bose-Einstein condensate

Peng Dong Du, Hui Tang, Jun Zhang, Wenxian Zhang

Published May 22, 2023• 0 citations
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Abstract

Benchmarking a high-precision quantum operation is a big challenge for many quantum systems in the presence of various noises as well as control errors. Here we propose an $O(1)$ benchmarking of a dynamically corrected rotation by taking quantum advantage of a squeezed spin state in a spin-1 Bose-Einstein condensate (BEC). Our analytical and numerical results show that tiny rotation infidelity, defined by $1\ensuremath{-}F$ with $F$ the rotation fidelity, can be calibrated in the order of $1/{N}^{2}$ by only several measurements of the rotation error for $N$ atoms in an optimally squeezed spin state. Such an $O(1)$ benchmarking is possible not only in a spin-1 BEC but also in other many-spin or many-qubit systems if a squeezed or entangled state is available.

DOI
10.1103/physreva.107.053315

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Benchmarking a high-precision quantum operation is a big challenge for many quantum systems in the presence of various noises as well as control errors. Here we propose an O(1)O(1)O(1) benchmarking of a dynamically corrected rotation by taking quantum advantage of a squeezed spin state in a spin-1 Bose-Einstein condensate (BEC). Our analytical and numerical results show that tiny rotation infidelity, defined by 1\ensuremath−F1\ensuremath{-}F1\ensuremath−F with FFF the rotation fidelity, can be calibrated in the order of 1/N21/{N}^{2}1/N2 by only several measurements of the rotation error for NNN atoms in an optimally squeezed spin state. Such an O(1)O(1)O(1) benchmarking is possible not only in a spin-1 BEC but also in other many-spin or many-qubit systems if a squeezed or entangled state is available.
Spin squeezed states are a class of entangled states of spins that have practical applications to precision measurements. In recent years spin squeezing with one-axis twisting (OAT) has been demonstrated experimentally with spinor Bose-Einstein condensates (BECs) with more than 103{10}^{3}103 atoms. Although the noise is below the standard quantum limit, the OAT scheme cannot reduce the noise down to the ultimate Heisenberg limit. Here we propose an experimentally feasible scheme based on optimized quantum control to greatly enhance the performance of OAT to approach the Heisenberg limit, requiring only an OAT Hamiltonian and the use of several coherent driving pulses. The scheme is robust against technical noise and can be readily implemented for spinor BECs or trapped ions with current technology.
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.
We report dispersive spin shot noise measurement of a Bose-Einstein condensate (BEC). While dispersive probing has been used for quantum spin noise measurement of thermal and cold gases for decades, confirmative measurement of shot noise of real spin, i.e., the linear dependence of the spin variance on the number of atoms in a BEC, has been lacking. Here, we demonstrate precise spin noise measurement of a BEC of rubidium atoms at the spin shot noise level by polarization rotation using a two-color probe at optimal detunings, with power balance stabilization to suppress probe-induced excess spin noise. This work opens the possibility for the unexplored study of quantum spin fluctuations in multicomponent or spinor BECs and offers an approach to improve spin measurement precision, which is relevant to atomic spin-based sensors.
Exotic types of magnetic order and phases resulting from collective behaviour of quantum spins are an important focus of many-body physics. Nematic or quadrupolar ordering of spins is one such example [1], which breaks O(3) rotational symmetry, has no magnetic moment and is analogous to the well-known ordering of molecules in nematic phases of liquid crystals [2]. Spin nematic phases have been posited for a variety of condensed matter systems including frustrated quantum magnets [3–5], and heavyfermion [6] and iron-based superconductors [7], although they are challenging to detect directly [8]. Spin-1 atomic Bose-Einstein condensates [9– 11] provide a natural system to investigate spinnematic quantum phases with a key advantage that the nematic tensor is directly measurable. Here, we measure spin-nematic fluctuations in a spin-1 condensate following a quench through a nematic to ferromagnetic quantum phase transition and observe quadrature squeezing in the variance of the fluctuations up to −8.3 −0.7 dB (−10.3 −0.9 dB corrected for detection noise) below the standard quantum limit. Previous work in atomic squeezing has employed two-level systems exhibiting SU(2) symmetry on the Bloch sphere [12, 13], while the squeezing observed here is an example of squeezing in an SU(3) system. These results demonstrate spin-nematic dynamics in the quantum regime and could form the basis of a quantum-enhanced magnetometer.
This paper reviews quantum spin squeezing, which characterizes the sensitivity of a state with respect to SU(2) rotations, and is significant for both entanglement detection and high-precision metrology. We first present various definitions of spin squeezing parameters, explain their origin and properties for typical states, and then discuss spin-squeezed states produced with nonlinear twisting Hamiltonians. Afterwards, we explain pairwise correlations and entanglement in spin-squeezed states, as well as the relations between spin squeezing and quantum Fisher information, where the latter plays a central role in quantum metrology. We also review the applications of spin squeezing for detecting quantum chaos and quantum phase transitions, as well as the influence of decoherence on spin squeezing. Finally, we review several experimental realizations of spin squeezing, as well as their corresponding theoretical backgrounds, including: producing spin-squeezed states via particle collisions in Bose-Einstein condensates, transferring photon squeezing to atomic ensembles, and generating spin squeezing via quantum non-demolition measurements.
Squeezed states play a key role in diverse frontiers of quantum physics. Geometrically squeezed states, a squeezed state in the orbital phase space of rotating Bose-Einstein condensates (BEC), have been conventionally generated by anisotropic trapping potentials. In this work, we propose a different route to generate geometric squeezing via spin-orbit coupling (SOC) in a pseudospin-1/2 BEC. We show that the SOC enables effective two-phonon transitions within the lowest Landau level via virtual spin-flip processes, leading to exponential squeezing dynamics in both spin components. Furthermore, by applying a π/2π/2π/2 spin rotation, the two spin channels can be coherently coupled to produce two-mode geometric squeezing. We also investigate the influence of interatomic interactions on squeezing performance and identify parameters where robust squeezing can be achieved. Our work provides a viable pathway to realize and manipulate geometric squeezing in spinor quantum gases.