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Physical Review A

Spin squeezing in a driven Bose-Einstein condensate

S. D. Jenkins, T. A. B. Kennedy

Published Oct 30, 2002• 21 citations
Publisher

Abstract

We consider a collection of atoms prepared in a Bose-Einstein condensate which interact via two-body elastic collisions. A resonant driving field couples two internal states which together constitute an effective spin 1/2 system for each atom, and from which a total spin for the gas can be defined. It is shown that in the limit of strong driving, the system dynamics reduces to a mechanism for spin squeezing similar to that of a recent proposal for undriven condensates. However, we find that the conditions for spatial stability in our driven system are complementary to those of the undriven system. Reasons for this difference, associated with the physics of dressed atom collisions, are discussed along with conditions for preparing and observing the spin squeezed state.

DOI
10.1103/physreva.66.043621

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We consider a collection of atoms prepared in a Bose-Einstein condensate which interact via two-body elastic collisions. A resonant driving field couples two internal states which together constitute an effective spin 1/2 system for each atom, and from which a total spin for the gas can be defined. It is shown that in the limit of strong driving, the system dynamics reduces to a mechanism for spin squeezing similar to that of a recent proposal for undriven condensates. However, we find that the conditions for spatial stability in our driven system are complementary to those of the undriven system. Reasons for this difference, associated with the physics of dressed atom collisions, are discussed along with conditions for preparing and observing the spin squeezed state.
We analyze the dynamical stability of common spatial, or breathe-together, modes for a system of two trapped interacting Bose-Einstein condensates, when the condensates are resonantly coupled by a strong driving field. We show analytically that the dynamical stability is governed by a set of dressed atom collision parameters, and that the driving field typically destabilizes breathe-together modes which are stable in the absence of driving and vice versa. By means of numerical solutions we illustrate the consequences of this phenomenon for a number of interacting condensates consisting of pairs of ground hyperfine states of both sodium and rubidium.
The evolution of an interacting two-component Bose-Einstein condensate from an initial phase state leads to a spin squeezed state that may be used in atomic clocks to increase the signal-to-noise ratio, opening the way to quantum metrology. The efficiency of spin squeezing is limited by the finite temperature of the gas, as was shown theoretically in a spatially homogeneous system. Here we determine the limit of spin squeezing in the realistic trapped case, with classical field simulations, and with a completely analytical treatment that includes the quantum case.
We study the spin squeezing in a spin-1/2 Bose-Einstein condensates (BEC) with Raman-induced spin-orbit coupling (SOC). Under the condition of two-photon resonance and weak Raman coupling strength, the system possesses two degenerate ground states, using which we construct an effective two-mode model. The Hamiltonian of the two-mode model takes the form of the one-axis-twisting Hamiltonian, which is known to generate spin squeezing. More importantly, we show that the SOC provides a convenient control knob to adjust the spin nonlinearity responsible for spin squeezing. Specifically, the spin nonlinearity strength can be tuned to be comparable to the two-body density-density interaction, and hence is much larger than the intrinsic spin-dependent interaction strength in conventional two-component BEC systems such as 87Rb^{87}\mathrm{Rb}87Rb and 23Na^{23}\mathrm{Na}23Na in the absence of the SOC. We confirm the spin squeezing by carrying out a fully beyond-mean-field numerical calculation using the truncated Wigner method. Additionally, the experimental implementation is also discussed.
Abstract We derive from first principles the experimentally observed effective dynamics of a spinor Bose gas initially prepared as a Bose–Einstein condensate and then left free to expand ballistically. In spinor condensates, which represent one of the recent frontiers in the manipulation of ultra-cold atoms, particles interact with a two-body spatial interaction and a spin–spin interaction. The effective dynamics is well-known to be governed by a system of coupled semi-linear Schrödinger equations: we recover this system, in the sense of marginals in the limit of infinitely many particles, with a mean-field re-scaling of the many-body Hamiltonian. When the resulting control of the dynamical persistence of condensation is quantified with the parameters of modern observations, we obtain a bound that remains quite accurate for the whole typical duration of the experiment.
The production of large-scale entangled states is one of the main goals of next-generation quantum technologies, with an immediate potential for applications in the context of entanglement-assisted quantum sensing. A very promising platform to achieve this goal is offered by ultracold spinor gases, made of atoms with a large internal spin sensitive to magnetic fields. Here we show that the native spin-changing collisions in a spinor Bose-Einstein condensate, combined with an arbitrary quadratic Zeeman shift, can generate scalable spin squeezing in the collective spin of the ensemble, following the universal paradigm of the celebrated one-axis-twisting model. Squeezing dynamics is driven by the quadratic Zeeman shift when this shift is small; and by the spin-changing collisions for large shifts, in the form of stroboscopic squeezing. Turning off the Zeeman shift freezes out the collective-spin dynamics, so that the ensuing collective spin dynamics can be uniquely governed by an external field to be sensed. Our theoretical results pave the way for the use of spinor Bose gases with a large spin in fundamental studies of entanglement, as well as in advanced metrological applications.