Spin-mixing dynamics of a spinor Bose-Einstein condensate

Pu, Han; Law, C. K.; Raghavan, S.; Eberly, J. H.; Bigelow, N. P.

doi:10.1103/physreva.60.1463

Cited by 239 publications

(267 citation statements)

References 26 publications

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“…In this case, the non-trivial dynamical evolution of the system occurs only in the internal spin variables, and the mean-field dynamics of the system can be described by a non-rigid pendulum similar to the two-site Bose-Hubbard model 20,21 . The system is fully integrable in both the quantum 22 and classical 21,23 limits, and provides the opportunity to explore non-equilibrium quantum dynamics that are not captured by mean-field approaches, and can be solved exactly with Schrödinger's equation. The condensate is prepared in a state corresponding to a hyperbolic fixed point in the spin-nematic phase space.…”

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confidence: 99%

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Non-equilibrium dynamics of an unstable quantum pendulum explored in a spin-1 Bose–Einstein condensate

et al. 2012

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A pendulum prepared perfectly inverted and motionless is a prototype of unstable equilibrium and corresponds to an unstable hyperbolic fixed point in the dynamical phase space. Here, we measure the non-equilibrium dynamics of a spin-1 Bose-Einstein condensate initialized as a minimum uncertainty spin-nematic state to a hyperbolic fixed point of the phase space. Quantum fluctuations lead to non-linear spin evolution along a separatrix and non-Gaussian probability distributions that are measured to be in good agreement with exact quantum calculations up to 0.25 s. At longer times, atomic loss due to the finite lifetime of the condensate leads to larger spin oscillation amplitudes, as orbits depart from the separatrix. This demonstrates how decoherence of a many-body system can result in apparent coherent behaviour. This experiment provides new avenues for studying macroscopic spin systems in the quantum limit and for investigations of important topics in non-equilibrium quantum dynamics.

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confidence: 99%

“…At finite fields, the dynamics are similar 25,26 , although they occur on a timescale favourable for experimental observation. In both cases, the evolution occurs along a separatrix of the phase space and is driven by quantum fluctuations that are absent from the mean-field theory solutions 23,26 .…”

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Non-equilibrium dynamics of an unstable quantum pendulum explored in a spin-1 Bose–Einstein condensate

et al. 2012

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“…The evolution toward ferromagnetism from the |m z = 0 state under the conditions q < |c 2 |n is a form of dynamical instability in a spinor BEC [12,13,14,15]. This instability is a consequence of coherent collisional spin mixing in which pairs of atoms in the |m z = 0 state collide inelastically to produce atoms in the |m z = ±1 states [3,4,9,16].…”

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Spontaneous symmetry breaking in a quenched ferromagnetic spinor Bose–Einstein condensate

Sadler

Higbie²,

Leslie³

et al. 2006

Nature

928

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A central goal in condensed matter and modern atomic physics is the exploration of manybody quantum phases and the universal characteristics of quantum phase transitions in so far as they differ from those established for thermal phase transitions. Compared with condensedmatter systems, atomic gases are more precisely constructed and also provide the unique opportunity to explore quantum dynamics far from equilibrium. Here we identify a second-order quantum phase transition in a gaseous spinor BoseEinstein condensate, a quantum fluid in which superfluidity and magnetism, both associated with symmetry breaking, are simultaneously realized. 87 Rb spinor condensates were rapidly quenched across this transition to a ferromagnetic state and probed using in-situ magnetization imaging to observe spontaneous symmetry breaking through the formation of spin textures, ferromagnetic domains and domain walls. The observation of topological defects produced by this symmetry breaking, identified as polar-core spin-vortices containing non-zero spin current but no net mass current, represents the first phase-sensitive in-situ detection of vortices in a gaseous superfluid.Most ultracold atomic gases consist of atoms with nonzero total angular momentum denoted by the quantum number F , which is the sum of the total electronic angular momentum and nuclear spin. In spinor atomic gases, such as F = 1 and F = 2 gases of 23 Na [1, 2] and 87 Rb [3,4], all magnetic sublevels representing all orientations of the atomic spin may be realized [5]. The phase coherent portion of a Bose-Einsein condensed spinor gas is described by a vector order parameter and therefore exhibits spontaneous magnetic ordering. Nevertheless, considerable freedom remains for the type of ordering that can occur. For 87 Rb F = 1 spinor gases, the spindependent energy per particle in the condensate is the sum of two terms, c 2 n F 2 + q F 2 z , where F denotes the dimensionless spin vector operator. The first term describes spin-dependent interatomic interactions, with n being the number density and c 2 = (4π 2 /3m)(a 2 − a 0 ) depending on the atomic mass m and the s-wave scattering lengths a f for collisions between pairs of particles with total spin f [6,7]. Given c 2 < 0 for our system [3,4,8,9], the interaction term alone favors a ferromagnetic phase with broken rotational symmetry. The second term describes a quadratic Zeeman shift in our experiment, with q = (h × 70 Hz/G 2 )B 2 at a magnetic field of magnitude B [10]. This term favors instead a scalar phase with no net magnetization, i.e. a condensate in the |m z = 0 magnetic sublevel. These phases are divided by a second-order quantum phase transition at q = 2|c 2 |n.This article describes our observation of spontaneous symmetry breaking in a 87 Rb spinor BEC that is rapidly quenched across this quantum phase transition. Nearlypure spinor Bose-Einstein condensates were prepared in the scalar |m z = 0 phase at a high quadratic Zeeman shift (q ≫ 2|c 2 |n). By rapidly reducing the magnitude of the applied magneti...

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“…For atoms in the F = 1 ground state manifold, the presence of Zeeman degeneracy and spin dependent atom-atom interactions [9,10,11,15,16,17,18,19] leads to interesting condensate spin dynamics. In this article, we study spin mixing inside a spin-1 condensate [17,19,20], focusing on the interaction-driven coherent oscillations within a mean field description. Unlike the pioneering studies on this subject as in Refs.…”

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Coherent spin mixing dynamics in a spin-1 atomic condensate

et al. 2005

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We study the coherent off-equilibrium spin mixing inside an atomic condensate. Using mean field theory and adopting the single spatial mode approximation (SMA), the condensate spin dynamics is found to be well described by that of a nonrigid pendulum, and displays a variety of periodic oscillations in an external magnetic field. Our results illuminate several recent experimental observations and provide critical insights into the observation of coherent interaction-driven oscillations in a spin-1 condensate. Bose-Einstein condensation (BEC) has been one of the most active topics in physics for over a decade, and yet interest in this field remains impressively high. Recent experiments showcase the rich versatility of control over the atomic superfluid, e.g. the BEC-BCS crossover [1,2], quantized vortices [3,4,5], condensates in optical lattices [6], and low dimensional quantum gases [7,8]. While most of these efforts involve condensates of atoms in a single Zeeman state, activities in spinor condensates [9,10] have recently received significant boost with the addition of three new spin-1 experiments [11,12,13,14].In a spinor condensate, atomic hyperfine spin degree of freedom becomes accessible with the use of a far-off resonant optical trap instead of a magnetic trap. For atoms in the F = 1 ground state manifold, the presence of Zeeman degeneracy and spin dependent atom-atom interactions [9,10,11,15,16,17,18,19] leads to interesting condensate spin dynamics. In this article, we study spin mixing inside a spin-1 condensate [17,19,20], focusing on the interaction-driven coherent oscillations within a mean field description. Unlike the pioneering studies on this subject as in Refs. [17,19], we will highlight the important role of an external magnetic field, which is present in all experiments to date.Recently, a beautiful experiment has finally observed the long predicted Josephson type coherent nonlinear oscillations with a scalar condensate in a spatial double well potential [21].Although spin mixing driven by the internal spindependent interaction (not of the nature of a Rabi oscillation as driven by an external field [22,23]), has been observed in both F = 1 and F = 2 condensates [9,12,14,24], the coherence of this process has not yet been investigated. Over-damped single oscillations in spin populations have been observed in earlier experiments [24] although their interpretation has been limited because evolution from the initial (meta-stable) states was noise-driven. The main experimental obstacles to observe more oscillations are the dissipative atomic collisions among the condensed atoms and the decoherence collisions with noncondensed atoms [12,24]. A promising future direction relies on increased atomic detection sensitivity, thus the use of smaller condensates as in the experiment of Ref. [21], with lower number densities and at lower temperatures, two favorable conditions for the single spatial mode approximation (SMA) [17,19].The initial atomic population distribution in Fig. 1 corresponds to the (equi...

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Spin-mixing dynamics of a spinor Bose-Einstein condensate

Cited by 239 publications

References 26 publications

Non-equilibrium dynamics of an unstable quantum pendulum explored in a spin-1 Bose–Einstein condensate

Non-equilibrium dynamics of an unstable quantum pendulum explored in a spin-1 Bose–Einstein condensate

Spontaneous symmetry breaking in a quenched ferromagnetic spinor Bose–Einstein condensate

Coherent spin mixing dynamics in a spin-1 atomic condensate

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