Mapping the phase diagram of spinor condensates via adiabatic quantum phase transitions

Jiang, Jie; Zhao, Lichao; Webb, Micah; Liu, Y.

doi:10.1103/physreva.90.023610

Cited by 33 publications

(48 citation statements)

References 24 publications

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“…Spin fluctuations show a steady increase after an initial, relatively rapid growth [ Fig. 4(g)], which we attribute to the heating effect of the microwave dressing [33]. The dissociation of a singly charged vortex involves spin texture formation as well as magnetized core development, as depicted in Fig.…”

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confidence: 84%

Half-Quantum Vortices in an Antiferromagnetic Spinor Bose-Einstein Condensate

et al. 2015

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We report on the observation of half-quantum vortices (HQVs) in the easy-plane polar phase of an antiferromagnetic spinor Bose-Einstein condensate. Using in situ magnetization-sensitive imaging, we observe that pairs of HQVs with opposite core magnetization are generated when singly charged quantum vortices are injected into the condensate. The dynamics of HQV pair formation is characterized by measuring the temporal evolutions of the pair separation distance and the core magnetization, which reveals the short-range nature of the repulsive interactions between the HQVs. We find that spin fluctuations arising from thermal population of axial magnon excitations do not significantly affect the HQV pair formation dynamics. Our results demonstrate the instability of a singly charged vortex in the antiferromagnetic spinor condensate. In a scalar superfluid, the supercurrent circulation around quantum vortices is quantized in units of h/m due to U (1) gauge symmetry [1], where h is the Planck constant and m is particle mass. However, when a superfluid possesses an internal spin degree of freedom, there is an intriguing possibility for the superfluid to host quantum vortices of a fractional circulation of h/m. The superfluid phase interwinds with the spin orientation and a new relation is imposed on the supercurrent circulation in connection with spin texture [2]. Fractional quantum vortices are of particular interest in two-dimensional (2D) superfluidity. In the absence of long-range order in two dimensions [3], the superfluid phase transition in 2D is associated with vortex-antivortex pairing as described by the Berezinskii-Kosterlitz-Thouless (BKT) theory [4,5]. Hence fractional quantum vortices, introduced as new point defects, represent an interesting opportunity to explore for exotic superfluid phases, possibly beyond the BKT physics.Quantum vortices having h/2m circulation, so-called half-quantum vortices (HQVs) have been experimentally observed in spinor superfluid systems such as excitonpolariton condensates [6][7][8] and triplet superconductors [9]. In previous cold atom experiments, HQV states were created with an optical method in two-component Bose-Einstein condensates (BECs) [10], where the two components are not symmetric in terms of interactions. Recently, a spin-1 BEC with antiferromagnetic interactions has been considered with great interest because HQVs are topologically allowed in the polar phase of the system [11][12][13]. Theoretical studies predicted an anomalous superfluid density jump at the phase transition in two dimensions [14][15][16] as well as a new superfluid state that has completely broken spin ordering [17,18].In this Letter, we report on the observation of HQVs in the easy-plane polar phase of an antiferromagnetic spinor BEC of 23 Na atoms. Using magnetization-sensitive imaging, we observe that pairs of HQVs with opposite core magnetization are generated when singly charged quantum vortices are injected into the condensate. The temporal evolutions of the pair separation distance and t...

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confidence: 84%

Half-Quantum Vortices in an Antiferromagnetic Spinor Bose-Einstein Condensate

et al. 2015

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“…φ mF = 0 ( = 0) in the MI (SF) phase. An antiferromagenetic F = 1 spinor BEC of zero magnetization forms a polar superfluid in equilibrium with S = 0 [2,23,24]. There are two types of polar superfluids: the longitudinal polar (LP) state with (φ 1 , φ 0 , φ −1 ) = √ ρ s (0, 1, 0) and the transverse polar…”

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confidence: 99%

First-order superfluid-to-Mott-insulator phase transitions in spinor condensates

Jiang¹,

Zhao²,

Wang³

et al. 2016

Phys. Rev. A

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We observe evidence of first-order superfluid to Mott-insulator quantum phase transitions in a lattice-confined antiferromagnetic spinor Bose-Einstein condensate. The observed signatures include hysteresis effect and significant heatings across the phase transitions. The nature of the phase transitions is found to strongly depend on the ratio of the quadratic Zeeman energy to the spindependent interaction. Our observations are qualitatively understood by the mean field theory, and in addition suggest tuning the quadratic Zeeman energy is a new approach to realize superfluid to Mott-insulator phase transitions.PACS numbers: 67.85. Fg, 03.75.Kk, 03.75.Mn, 05.30.Rt A quantum phase transition from a superfluid (SF) to a Mott-insulator (MI) was realized in a scalar BoseEinstein condensate (BEC) trapped by three-dimensional (3D) optical lattices around a decade ago [1]. Marking an important milestone, this achievement has stimulated tremendous efforts to apply highly controllable ultracold bosonic and fermionic systems in studying condensed matter models [2][3][4][5][6]. The SF-MI transitions have been confirmed in various scalar BEC systems via different techniques that can efficiently control the ratio of interatomic interactions to the mobility of atoms [1,[5][6][7]. One well-known approach to simultaneously enhance interatomic interactions and suppress atomic motion is by raising the depth of an optical lattice [1]. Another convenient method is to manipulate interactions with a magnetically tuned Feshbach resonance [7]. A third technique is to control the hopping energy of bosonic atoms by periodically shaking the lattice [6]. Spinor BECs, on the other hand, possess an additional spin degree of freedom, leading to a range of phenomena absent in scalar BECs [8][9][10][11][12][13]. One important prediction is the existence of the first-order SF-MI phase transitions in latticetrapped antiferromagnetic spinor BECs [2,11,[13][14][15][16][17]. In contrast, the phase transitions can only be second order in scalar BECs and ferromagnetic spinor BECs [2,5,17].In this paper, SF-MI phase transitions are studied in sodium antiferromagnetic spinor BECs confined by cubic optical lattices. We observe hysteresis effect and substantial heating across the phase transitions, which indicate the existence of meta-stable states and associated firstorder transitions. In the ground state of the spinor BECs, the nature of the SF-MI transitions is found to be determined by the competition between the quadratic Zeeman energy q B and the spin-dependent interaction U 2 . At low magnetic fields where U 2 dominates, signatures of firstorder transitions are observed. In the opposite limit, the transitions appear to be second order and resemble those occurring in scalar BECs. These qualitative features are explained by our mean-field (MF) calculations. We also study the phase transitions with an initial meta-stable state and observe stronger heatings across all magnetic fields. Furthermore, our data indicate that a new technique to realize SF-M...

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“…In contrast to a scalar BEC, a spinor BEC has unique advantages due to an additional spin degree of freedom. The SF-MI phase transition is predicted to be remarkably different in spinor BECs, i.e., the transition may be first (or second) order around the tip of each Mott lobe for an even (or odd) occupation number in lattice-trapped antiferromagnetic spinor BECs [1,10].Spin-mixing dynamics and phase diagrams of spinor BECs in free space, as a result of spin-dependent interactions and quadratic Zeeman energy q B , have been well studied with sodium atoms [11][12][13][14][15][16][17] and rubidium atoms [18][19][20][21]. Richer spin dynamics are predicted to exist in lattice-trapped spinor BECs, which allow for a number of immediate applications.…”

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confidence: 99%

“…Spin-mixing dynamics and phase diagrams of spinor BECs in free space, as a result of spin-dependent interactions and quadratic Zeeman energy q B , have been well studied with sodium atoms [11][12][13][14][15][16][17] and rubidium atoms [18][19][20][21]. Richer spin dynamics are predicted to exist in lattice-trapped spinor BECs, which allow for a number of immediate applications.…”

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confidence: 99%

Antiferromagnetic Spinor Condensates in a Two-Dimensional Optical Lattice

et al. 2015

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We experimentally demonstrate that spin dynamics and the phase diagram of spinor condensates can be conveniently tuned by a two-dimensional optical lattice. Spin population oscillations and a lattice-tuned separatrix in phase space are observed in every lattice where a substantial superfluid fraction exists. In a sufficiently deep lattice, we observe a phase transition from a longitudinal polar phase to a broken-axisymmetry phase in steady states of lattice-confined spinor condensates. The steady states are found to depend sigmoidally on the lattice depth and exponentially on the magnetic field. We also introduce a phenomenological model that semi-quantitatively describes our data without adjustable parameters.PACS numbers: 67.85. Fg, 03.75.Kk, 03.75.Mn, 05.30.Rt A spinor Bose-Einstein condensate (BEC) confined in optical lattices has attracted much attention for its abilities to systematically study, verify, and optimize condensed matter models [1][2][3]. For instance, it can quantum simulate the Laughlin-type wavefunctions appearing in the fractional quantum Hall systems [4,5]. A better understanding of these models may directly lead to engineering revolutionary materials. An optical lattice has been a versatile technique to enhance interatomic interactions and control the mobility of atoms [6][7][8]. Atoms held in a shallow lattice can tunnel freely among lattice sites and form a superfluid (SF) phase. The tunneling rate is exponentially suppressed while the on-site atomatom interaction is increased in a deeper lattice. This may result in a transition from a SF phase to a Mottinsulator (MI) phase at a critical lattice depth, which has been confirmed in various scalar BEC systems [6][7][8][9]. In contrast to a scalar BEC, a spinor BEC has unique advantages due to an additional spin degree of freedom. The SF-MI phase transition is predicted to be remarkably different in spinor BECs, i.e., the transition may be first (or second) order around the tip of each Mott lobe for an even (or odd) occupation number in lattice-trapped antiferromagnetic spinor BECs [1,10].Spin-mixing dynamics and phase diagrams of spinor BECs in free space, as a result of spin-dependent interactions and quadratic Zeeman energy q B , have been well studied with sodium atoms [11][12][13][14][15][16][17] and rubidium atoms [18][19][20][21]. Richer spin dynamics are predicted to exist in lattice-trapped spinor BECs, which allow for a number of immediate applications. These include constructing a novel quantum-phase-revival spectroscopy driven by a competition between spin-dependent and spin-independent interactions, understanding quantum magnetism, directly detecting spin-dependent three-body and higher-body interactions, and realizing massive entanglement [1,3,22]. However, dynamics of latticetrapped spinor BECs have remained to be less explored, and most of such experimental studies have been carried out in ferromagnetic 87 Rb spinor BECs [23][24][25][26].In this paper, we experimentally demonstrate that a two-dimensional (2D) optical latt...

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Mapping the phase diagram of spinor condensates via adiabatic quantum phase transitions

Cited by 33 publications

References 24 publications

Half-Quantum Vortices in an Antiferromagnetic Spinor Bose-Einstein Condensate

Half-Quantum Vortices in an Antiferromagnetic Spinor Bose-Einstein Condensate

First-order superfluid-to-Mott-insulator phase transitions in spinor condensates

Antiferromagnetic Spinor Condensates in a Two-Dimensional Optical Lattice

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