Quantum correlation protection through spin self-rephasing in a one-dimensional Bose gas

Konrad Szymański and Krzysztof Pawłowski

Phys. Rev. A 101, 013432 – Published 28 January 2020

Abstract

A system consisting of a number of trapped two-level atoms in the presence of external inhomogeneous magnetic field undergoes dephasing: classically, since each atom feels a different field along its trajectory, the pseudospin rotation rates differ; as a result the average spin decays. It has been demonstrated in recent years that in the case of systems initiated in the atomic coherent state such spin dephasing can be prevented by tuning the interaction between the atoms to induce so-called spin self-rephasing. While the effect has been studied theoretically from a semiclassical point of view, a quantum-mechanical description is limited. In this paper we provide a numerical simulation of an ab initio model and provide realistic examples of spin self-rephasing used to counteract the effect of inhomogeneous magnetic field. We found that the spin self-rephasing method can be also used to prevent atomic squeezed states from decoherence: while the dephasing inhibition is lower as compared with the case of coherent states, it is still comparatively large and may be useful in real interferometric scenarios.

Received 30 July 2019
Revised 7 January 2020

DOI:https://doi.org/10.1103/PhysRevA.101.013432

Physics Subject Headings (PhySH)

Atom interferometry Bose gases Decoherence in quantum gases

Atomic, Molecular & Optical

Authors & Affiliations

Konrad Szymański

Center for Theoretical Physics PAS, Aleja Lotników 32/46, 02-668 Warszawa, Poland and Marian Smoluchowski Institute of Physics, ul. Łojasiewicza 11, 30-348 Kraków, Poland

Krzysztof Pawłowski

Center for Theoretical Physics PAS, Aleja Lotników 32/46, 02-668 Warszawa, Poland

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Vol. 101, Iss. 1 — January 2020

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Images

Figure 1
Decay of the coherence (2) of ideal gas in a thermal state. The decay is due to a quadratic magnetic field with $b_{2} = 0.05$ (in oscillatory units), without the linear term ( $b_{1} = 0$ ). Temperature is $k_{B} T = 10 ℏ ω$ and number of atoms is equal to $N = 100$ in all three considered cases.
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Figure 2
Energy diagram illustrating the dephasing and the spin self-rephasing mechanisms for (a) two and (b) three bosons. Two (pseudo)spins can be either in the completely symmetric space (triplet) or in the singlet state; the nonuniform magnetic field couples the two subspaces. As the subspaces have the same energies, this coupling leads to a transfer of atoms out of the symmetric subspace, i.e., to the dephasing. In the case of higher number of atoms the nonuniform magnetic field acts similarly, coupling the maximal and lower total spin subspaces. Interactions between particles separate the total spin subspaces [ $J = 1$ and 0 in (a), $J = 3 / 2$ and two copies of $J = 1 / 2$ in (b)], leading to smaller effective coupling. The figure is an adaptation of the figure and explanation given in [15].
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Figure 3
Top: Evolution of maximal spin population as a function of time for several interaction strengths denoted in the bottom image by dots (the noninteracting case is denoted by thick black line), $N = 5, k_{B} T = 3 ℏ ω$ , and quadratic inhomogeneity $b_{2} = 0.01$ . Quick decay followed by plateau is visible. Bottom: Preservation of trace for the same parameters for time $ω t = 50$ as a function of interactions parametrized by mean interaction strength $g$ and $c$ .
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Figure 4
Effect of interactions on preservation of the coherence $C$ . Total number of particles $N = 5$ , temperature $k_{B} T = 3 ℏ ω$ , and quadratic inhomogeneity $b_{2} = 0.01$ . Top: typical short-time evolution of $C$ for several interaction strengths denoted in the bottom image by dots; the noninteracting case is denoted by thick black line. As evidenced by the figure, it is possible to approximately double the time of decoherence (when the contrast attains half of its original value). Bottom: $〈 S_{x} 〉$ at $ω t = 50$ for various values of interaction strengths parametrized by $g$ and $c$ . Please note that the same interaction range is used in Fig. 3.
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Figure 5
Effect of interaction on preservation of squeezing parameter $ξ^{2}$ for various values of interaction strengths parametrized by $g$ and $c$ . The color is correlated with the time of decoherence $t$ at which squeezing parameter $ξ^{2}$ becomes larger than 1 as compared to the time of decoherence without interactions $t_{0}$ . The temperature $k_{B} T = 3 ℏ ω$ , quadratic inhomogeneity $b_{2} = 0.01$ , and total number of particles $N = 5$ (top) and $N = 10$ (bottom). In both cases the squeezing time [ $θ$ in Eq. (15)] is 0.05, leading to $ξ^{2} (N = 10) = 0.44$ and $ξ^{2} (N = 5) = 0.69$ at the beginning of the evolution. In the case of $N = 10$ it is possible to increase the time at which $ξ^{2}$ becomes higher than 1 by a factor of $75 %$ ; for $N = 5$ this time can be increased by about $60 %$ .
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Figure 6
Figure analogous to the bottom picture of Fig. 5 (preservation of squeezing parameter for $N = 10$ ); note the same range of interaction parameters. In order to prepare this picture, the simulation basis has been artificially restricted, effectively leading to ignoring of spatial dynamics. The oversimplified description leads to decoherence time delay of about 180%, far from 75% obtained with more accurate simulation.
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