Real-space mean-field theory of a spin-1 Bose gas in synthetic dimensions

Hurst, Hilary M.; Wilson, Justin H.; Pixley, J. H.; Spielman, I. B.; Natu, Stefan S.

doi:10.1103/physreva.94.063613

Cited by 16 publications

(19 citation statements)

References 31 publications

(66 reference statements)

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“…If we consider these results in the present context by considering the one dimensional model in Eq. ( 6), the superfluid wavefunction is qualitatively captured by the Gutzwiller or Gross-Pitaevskii approximations [60]. However, because of strong quantum fluctuation effects in one dimension, we expect that the striped superfluid would be better described by a three component Luttinger liquid (similar to the pseudospin-1/2 case, Ref.…”

Section: Modelmentioning

confidence: 95%

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Strong-coupling phases of the spin-orbit-coupled spin-1 Bose-Hubbard chain: Odd-integer Mott lobes and helical magnetic phases

et al. 2017

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We study the odd integer filled Mott phases of a spin-1 Bose-Hubbard chain and determine their fate in the presence of a Raman induced spin-orbit coupling which has been achieved in ultracold atomic gases; this system is described by a quantum spin-1 chain with a spiral magnetic field. The spiral magnetic field initially induces helical order with either ferromagnetic or dimer order parameters, giving rise to a spiral paramagnet at large field. The spiral ferromagnet-to-paramagnet phase transition is in a novel universality class, with critical exponents associated with the divergence of the correlation length ν ≈ 2/3 and the order parameter susceptibility γ ≈ 1/2. We solve the effective spin model exactly using the density matrix renormalization group, and compare with both a large-S classical solution and a phenomenological Landau theory. We discuss how these exotic bosonic magnetic phases can be produced and probed in ultracold atomic experiments in optical lattices.Strongly-correlated quantum spin chains are an interacting many-body system that have been an instrumental platform to develop an understanding of topological properties [1], Berry phase effects [2], and quantum phase transitions [3]. One of the paradigmatic theoretical models in this context is the spin-1 bilinear-biquadratic Heisenberg chain [2-4](J is the unit of energy) which supports several conceptually important phases and phase transitions [5][6][7][8][9][10][11][12][13][14]. The physics associated with the Hamiltonian in Eq. (1) is not only theoretically tantalizing, but is also directly accessible to experiments. For example, the antiferromagnetic spin-1 chain (cos θ > 0) has been probed experimentally in insulating quantum magnets [15][16][17] that possess wellisolated, quasi-one-dimensional chains of S = 1 local moments. Interestingly, ultracold atomic gases are a natural platform for realizing the complementary ferromagnetic spin-1 chain (cos θ < 0), where the system is an effective description of the Mott insulating spin-1 Bose-Hubbard model [18][19][20][21][22][23]. Solid state experiments always contain at least some disorder that breaks the spin chain into segments [16], while the cold atomic gas setting is essentially pristine with no disorder in principle, so that the theoretical model defined by Eq. (1) (as well as its generalizations) can be studied directly. Until recently, it has been difficult to realize magnetic ordering in ultra-cold atomic gases [24,25], and a crucial element of physics is developing a theoretical understanding of the available strongly correlated phases. A virtue of the flexibility and the precise control in atomic and molecular experiments is that various physical effects can be engineered simulating desired features of solid-state systems despite the vastly different setting (i.e. atoms versus solids). Along these lines, recent experiments on cold atomic gases have demonstrated that, despite the atoms being electrically neutral, spin orbit coupling (SOC) can be engineered using two counter propagating...

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Section: Modelmentioning

confidence: 95%

“…At moderate U 0 /t the spin density wave order is destroyed and the superfluid condenses at a non-zero momentum only. Owing to strong lattice effects, this occurs on the edge of the Brilliouin zone [33,60]. Finally, a Mott transition occurs at even larger U 0 /t.…”

Section: Modelmentioning

confidence: 96%

Strong-coupling phases of the spin-orbit-coupled spin-1 Bose-Hubbard chain: Odd-integer Mott lobes and helical magnetic phases

et al. 2017

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“…Notably, while the interaction is short-range in real space, it is long-range in the synthetic dimension-a spin-independent interaction gives a leading part of the interaction in many atomic systems. This anisotropic nature of the interaction sharply contrasts with fractional quantum Hall (FQH) systems, and has been shown to lead to density waves [28][29][30], fractional charge pumping [29,31], helical liquids [28,30,[32][33][34][35], supersolids, pair superfliuds [36], and other interesting phenomena [37][38][39].…”

Section: Introductionmentioning

confidence: 99%

Devil's staircases in synthetic dimensions and gauge fields

Saito

Furukawa

2017

Phys. Rev. A

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We study interacting bosonic or fermionic atoms in a high synthetic magnetic field in two dimensions spanned by continuous real space and a synthetic dimension. Here, the synthetic dimension is provided by hyperfine spin states, and the synthetic field is created by laser-induced transitions between them. While the interaction is short-range in real space, it is long-range in the synthetic dimension in sharp contrast with fractional quantum Hall systems. Introducing an analog of the lowest-Landau-level approximation valid for large transition amplitudes, we derive an effective one-dimensional lattice model, in which density-density interactions turn out to play a dominant role. We show that in the limit of a large number of internal states, the system exhibits a cascade of crystal ground states, which is known as devil's staircase, in a way analogous to the thin-torus limit of quantum Hall systems.Comment: 9 pages, 4 figure

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“…[38] Also usages of the hyperfine spin states as short lattice dimension, known as the synthetic dimension, [44] to create spatially varying SOC gives rise to multiple density ordered SF phases such as the charge density or the spin density wave phases. [45] Although the different density ordered SF phases have been proposed for a spin-1 system using SOC, a specific concern is the possibility to study also the charge density wave (CDW) Mott insulating phase by employing a spin-1 BHM with non local nearest neighbour extended interactions apart from the usual onsite interaction, that may help in realizing the CDW phase. We feel such an extended interaction is relevant in the present context.…”

Section: Introductionmentioning

confidence: 99%

Spin‐1 Bose Hubbard Model with Nearest Neighbour Extended Interaction

Nabi

Basu

2017

Annalen der Physik

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A spinor (F = 1) Bose gas is studied in presence of a density-density interaction through a mean field approach and a perturbation theory for either sign of the spin dependent interaction, namely the antiferromagnetic (AF) and the ferromagnetic cases. In the AF case, the charge density wave (CDW) phase appears to be sandwiched between the Mott insulating (MI) and the supersolid phases for small values of the extended interaction strength. But the CDW phase completely occupies the MI lobe when the extended interaction strength is larger than a certain critical value related to the width of the MI lobes and hence opens up the possibilities of spin singlet and nematic CDW insulating phases. In the ferromagnetic case, the phase diagram shows similar features as that of the AF case and are in complete agreement with a spin-0 Bose gas. The perturbation expansion calculations nicely corroborate the mean field phase results in both these cases. Further, we extend our calculations in presence of a harmonic confinement and obtained the momentum distribution profile that is related to the absorption spectra in order to distinguish between different phases.

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Real-space mean-field theory of a spin-1 Bose gas in synthetic dimensions

Cited by 16 publications

References 31 publications

Strong-coupling phases of the spin-orbit-coupled spin-1 Bose-Hubbard chain: Odd-integer Mott lobes and helical magnetic phases

Strong-coupling phases of the spin-orbit-coupled spin-1 Bose-Hubbard chain: Odd-integer Mott lobes and helical magnetic phases

Devil's staircases in synthetic dimensions and gauge fields

Spin‐1 Bose Hubbard Model with Nearest Neighbour Extended Interaction

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