Direct observation of zitterbewegung in a Bose–Einstein condensate

LeBlanc, Lindsay J.; Beeler, Matthew; Jiménez-García, Karina; Perry, Abigail R.; Sugawa, Seiji; Williams, R. A.; Spielman, I. B.

doi:10.1088/1367-2630/15/7/073011

Cited by 175 publications

(166 citation statements)

References 38 publications

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“…However, such exotic motion has been simulated experimentally in different systems such as trapped ions [148], optical waveguide arrays [149] and BECs [17,21]. The motivation behind these experiments [17,148,149] is the preparation of the simplest Dirac system having one time and just one spatial dimension. Such a 1 + 1-dimensional Dirac system is described by a two-component spinor.…”

Section: Collective Dynamics: Zitterbewegungmentioning

confidence: 99%

“…After the first realization of a SOC BEC in 87 Rb, the NIST group used this system to explore partial wave scattering [16] and the phenomenon of Zitterbewegung (ZB) [17], to simulate spin Hall physics [18], and to gain control over the tunability of the SOC strength [19]. A University of Science and Technology of China (USTC) group measured the dipole oscillation in different phases of a SOC 87 Rb BEC [27], clarified finite temperature effects on the phase transition [28], measured roton-like collective excitations [29], and recently realized 2D SOC for bosons [30].…”

Section: Introductionmentioning

confidence: 99%

“…To set the stage, we will first briefly describe the experimental approaches to generate SOC [9,[16][17][18][19][20][21][22][23][24][25][26][27][28][29][31][32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

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Properties of spin–orbit-coupled Bose–Einstein condensates

et al. 2016

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The experimental and theoretical research of spin-orbit-coupled ultracold atomic gases has advanced and expanded rapidly in recent years. Here, we review some of the progress that either was pioneered by our own work, has helped to lay the foundation, or has developed new and relevant techniques. After examining the experimental accessibility of all relevant spin-orbit coupling parameters, we discuss the fundamental properties and general applications of spin-orbit-coupled Bose-Einstein condensates (BECs) over a wide range of physical situations. For the harmonically trapped case, we show that the ground state phase transition is a Dicke-type process and that spin-orbit-coupled BECs provide a unique platform to simulate and study the Dicke model and Dicke phase transitions. For a homogeneous BEC, we discuss the collective excitations, which have been observed experimentally using Bragg spectroscopy. They feature a roton-like minimum, the softening of which provides a potential mechanism to understand the ground state phase transition. On the other hand, if the collective dynamics are excited by a sudden quenching of the spin-orbit coupling parameters, we show that the resulting collective dynamics can be related to the famous Zitterbewegung in the relativistic realm. Finally, we discuss the case of a BEC loaded into a periodic optical potential. Here, the spin-orbit coupling generates isolated flat bands within the lowest Bloch bands whereas the nonlinearity of the system leads to dynamical instabilities of these Bloch waves. The experimental verification of this instability illustrates the lack of Galilean invariance in the system.

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Section: Collective Dynamics: Zitterbewegungmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Properties of spin–orbit-coupled Bose–Einstein condensates

et al. 2016

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“…Artificial electric and magnetic fields have been induced using lasers [3][4][5]. Moreover, these setups may be extended to generate non-Abelian fields, and in particular, spin-orbit coupling [6][7][8][9][10][11][12][13]. Synthetic fields may be generated as well in optical lattices, and recent experiments have created artificial staggered [14][15][16] and uniform [17,18] magnetic fields.…”

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confidence: 99%

Density-Dependent Synthetic Gauge Fields Using Periodically Modulated Interactions

et al. 2014

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We show that density-dependent synthetic gauge fields may be engineered by combining periodically modulated interactions and Raman-assisted hopping in spin-dependent optical lattices. These fields lead to a density-dependent shift of the momentum distribution, may induce superfluid-to-Mott insulator transitions, and strongly modify correlations in the superfluid regime. We show that the interplay between the created gauge field and the broken sublattice symmetry results, as well, in an intriguing behavior at vanishing interactions, characterized by the appearance of a fractional Mott insulator. DOI: 10.1103/PhysRevLett.113.215303 PACS numbers: 67.85.-d, 03.65.Vf, 03.75.Lm, 37.10.Jk The emulation of synthetic electromagnetism in cold neutral gases has attracted major interest [1,2]. Artificial electric and magnetic fields have been induced using lasers [3][4][5]. Moreover, these setups may be extended to generate non-Abelian fields, and in particular, spin-orbit coupling [6][7][8][9][10][11][12][13]. Synthetic fields may be generated as well in optical lattices, and recent experiments have created artificial staggered [14][15][16] and uniform [17,18] magnetic fields. These fields are, however, static, as they are not influenced by the atoms.The dynamical feedback between matter and gauge fields plays an important role in various areas of physics, ranging from condensed matter [19] to quantum chromodynamics [20], and its realization in cold lattice gases is attracting growing attention [21]. Schemes have been recently proposed for multicomponent lattice gases, such that the low-energy description of these systems is that of relevant quantum field theories [22][23][24][25][26][27][28][29][30][31]. The backaction of the atoms on the value of a synthetic gauge field is expected to lead to interesting physics, including statistically induced phase transitions and anyons in 1D lattices [32], and chiral solitons in Bose-Einstein condensates [33].Periodically modulated optical lattices open interesting possibilities for the engineering of lattice gases [16][17][18][34][35][36][37][38][39][40]. In particular, periodic lattice shaking results in a modified hopping rate [34][35][36], which has been employed to drive the superfluid (SF) to Mott insulator (MI) transition [37], to simulate frustrated classical magnetism [38], and to create tunable gauge potentials [16]. Interestingly, a periodically modulated magnetic field may be employed in the vicinity of a Feshbach resonance to induce periodically modulated interactions, which result in a nonlinear hopping rate that depends on the occupation differences at neighboring sites [41][42][43].In this Letter, we show that combining periodic interactions and Raman-assisted hopping may induce a densitydependent gauge field in 1D lattices. The created field results in a density-dependent shift of the momentum distribution that may be probed in time-of-flight (TOF) experiments. Moreover, contrary to the Peierls phase induced in shaken lattices [16], the created field cannot be ga...

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“…Experiments on ultracold atomic gases have started to explore analogous issues for SOC in Bose fluids, using Raman transitions to induce an equal Rashba-Dresselhaus SOC and a uniform Zeeman magnetic field [8][9][10][11][12][13][14][15][16] Motivated by the broad interest in understanding the interplay of SOC and strong correlations, and ongoing experimental efforts in ultracold gases, we focus here on two important questions. (a) How does the presence of a lattice and strong correlations modify the ground states of bosons with equal Rashba-Dresselhaus SOC?…”

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confidence: 99%

Thermal Phase Transitions of Strongly Correlated Bosons with Spin-Orbit Coupling

Hickey

Paramekanti

2014

Phys. Rev. Lett.

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Experiments on ultracold atoms have started to explore lattice effects and thermal fluctuations for two-component bosons with spin-orbit coupling (SOC). Motivated by this, we derive and study a tJ model for lattice bosons with equal Rashba-Dresselhaus spin-orbit coupling (SOC) and strong Hubbard repulsion in a uniform Zeeman magnetic field. Using the Gutzwiller ansatz, we find strongly correlated ground states with stripe superfluid (SF) order. We formulate a finite temperature generalization of the Gutzwiller method, and show that thermal fluctuations in the doped Mott insulator drive a two-step melting of the stripe SF, revealing a wide regime of a stripe normal fluid.Spin orbit coupling (SOC) underlies a diverse range of remarkable phases in solid state materials including topological insulators [1,2], quantum anomalous Hall insulators [3,4], and Skyrmion crystals [5], while its interplay with strong correlations is expected to lead to exotic topological Mott insulators [6,7]. Experiments on ultracold atomic gases have started to explore analogous issues for SOC in Bose fluids, using Raman transitions to induce an equal Rashba-Dresselhaus SOC and a uniform Zeeman magnetic field [8][9][10][11][12][13][14][15][16] Motivated by the broad interest in understanding the interplay of SOC and strong correlations, and ongoing experimental efforts in ultracold gases, we focus here on two important questions. (a) How does the presence of a lattice and strong correlations modify the ground states of bosons with equal Rashba-Dresselhaus SOC? (b) How do thermal fluctuations impact Bose superfluids with SOC? Our key results are the following. (i) At strong correlations, we derive an effective tJ model for lattice bosons with equal Rashba-Dresselhaus SOC and a uniform magnetic field. Using a zero temperature Gutzwiller ansatz, we show that this leads to strongly correlated variants of stripe and incommensurate SFs previously discussed in the continuum. However, unlike in the continuum, applying a large magnetic field leads to three distinct SFs (see Fig. 1(a,b)) depending on the SOC angle: (a) a zero momentum SF analogous to the continuum case, (b) a π-momentum SF, or (c) a π/2-momentum SF. (ii) At weaker field, strong interactions induce stripe order; in contrast to the continuum, the stripe order has significant higher harmonic content resulting in extra peaks in the momentum distribution as seen from Fig. 1(c,d). (iii) Previous work has considered thermal fluctuations of weakly interacting continuum bosons with SOC [26,27]. Here, to study strongly interacting lattice bosons, we formulate a stochastic Gutzwiller approach, which treats strong quantum correlations at mean field level, but retains full knowledge of spatial thermal fluctuations. The Monte Carlo (MC) technique introduced here is of broad applicability, being especially useful when the sign problem prevents quantum MC simulations, such as for frustrated bosons. (iv) Using this approach, we obtain the concrete temperature-doping phase diagram of spinor lattice bo...

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Direct observation of zitterbewegung in a Bose–Einstein condensate

Cited by 175 publications

References 38 publications

Properties of spin–orbit-coupled Bose–Einstein condensates

Properties of spin–orbit-coupled Bose–Einstein condensates

Density-Dependent Synthetic Gauge Fields Using Periodically Modulated Interactions

Thermal Phase Transitions of Strongly Correlated Bosons with Spin-Orbit Coupling

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