Quantum crystal growing: adiabatic preparation of a bosonic antiferromagnet in the presence of a parabolic inhomogeneity

Gammelmark, Søren; Eckardt, André

doi:10.1088/1367-2630/15/3/033028

Cited by 11 publications

(9 citation statements)

References 71 publications

(129 reference statements)

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“…This is reminiscent of the density-wave state discussed recently in Ref. 69. This could indicate a first order transition.…”

Section: Discussionsupporting

confidence: 65%

Dipoles on a two-leg ladder

Gammelmark¹,

Zinner²

2013

Phys. Rev. B

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We study polar molecules with long-range dipole-dipole interactions confined to move on a two-leg ladder for different orientations of the molecular dipole moments with respect to the ladder. Matrix product states are employed to calculate the many-body ground state of the system as function of lattice filling fractions, perpendicular hopping between the legs, and dipole interaction strength. We show that the system exhibits zig-zag ordering when the dipolar interactions are predominantly repulsive. As a function of dipole moment orientation with respect to the ladder, we find that there is a critical angle at which ordering disappears. This angle is slightly larger than the angle at which the dipoles are non-interacting along a single leg. This behavior should be observable using current experimental techniques.

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“…This is reminiscent of the density-wave state discussed recently in Ref. 69. This could indicate a first order transition.…”

Section: Discussionsupporting

confidence: 65%

Dipoles on a two-leg ladder

Gammelmark¹,

Zinner²

2013

Phys. Rev. B

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“…Adiabatic processes can dramatically lower the temperature of a system, if external parameters are slowly varied with respect to the level spacing between excited states of the system [5,[10][11][12][13][14][15][16]. Since adiabatic processes conserve entropy, one should select an initial state which can be prepared with very low entropy.…”

mentioning

confidence: 99%

Adiabatic cooling of bosons in lattices to magnetically ordered quantum states

Schachenmayer¹,

Weld²,

Miyake³

et al. 2015

Phys. Rev. A

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We suggest and analyze a scheme to adiabatically cool bosonic atoms to picokelvin temperatures which should allow the observation of magnetic ordering via superexchange in optical lattices. The starting point is a gapped phase called the spin Mott phase, where each site is occupied by one spin-up and one spin-down atom. An adiabatic ramp leads to an xy-ferromagnetic phase. We show that the combination of time-dependent density matrix renormalization group methods with quantum trajectories can be used to fully address possible experimental limitations due to decoherence, and demonstrate that the magnetic correlations are robust for experimentally realizable ramp speeds. Using a microscopic master equation treatment of light scattering in the many-particle system, we test the robustness of adiabatic state preparation against decoherence. Due to different ground-state symmetries, we also find a metastable state with xy-ferromagnetic order if the ramp crosses to regimes where the ground state is a z ferromagnet. The bosonic spin Mott phase as the initial gapped state for adiabatic cooling has many features in common with a fermionic band insulator, but the use of bosons should enable experiments with substantially lower initial entropies. A major goal in the field of ultracold atoms is to reach picokelvin temperatures in optical lattices and observe new spin-ordered quantum phases [1,2]. Such low temperatures are necessary due to the smallness of superexchange (second-order tunneling) matrix elements [3] which determine the transition temperature to magnetically ordered phases [4][5][6]. Realizing long-range magnetic ordering based on superexchange processes for mobile particles would open the door to the rich phase diagrams and out-of-equilibrium dynamics of the corresponding models [3]. It would also form the basis for quantum simulation of the low-temperature properties of models for mobile particles near spin-ordered phases [2,7]. However, despite encouraging recent experiments in which short-range magnetic correlations have been observed [8,9], the experimental temperatures remain too high for observation of long-range magnetic behavior driven by superexchange.The current strategy is to cool atoms by evaporative cooling, and then continue with some form of adiabatic cooling. Adiabatic processes can dramatically lower the temperature of a system, if external parameters are slowly varied with respect to the level spacing between excited states of the system [5,[10][11][12][13][14][15][16]. Since adiabatic processes conserve entropy, one should select an initial state which can be prepared with very low entropy.The use of adiabatic ramps starting from a band insulator of fermionic atoms has been proposed for production of a variety of states [11][12][13][14]. These involve a ramp from states with a large gap that can be prepared with low entropy to a state with a much smaller gap, and often spin ordering, generally making use of a superlattice potential to delocalize the atoms and select filling factors. For reali...

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“…Its relevance to many-body state preparation and adiabatic quantum computation was pointed out in [26,27], see as well [33]. This line of thinking has recently been applied to the adiabatic growth of an antiferromagnetic phase in a Mott insulator made of two atomic species [69].…”

Section: Defect Formation Beyond Scaling Lawsmentioning

confidence: 97%

Causality and non-equilibrium second-order phase transitions in inhomogeneous systems

del Campo,

Kibble,

Zurek

2013

Preprint

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When a second-order phase transition is crossed at fine rate, the evolution of the system stops being adiabatic as a result of the critical slowing down in the neighborhood of the critical point. In systems with a topologically nontrivial vacuum manifold, disparate local choices of the ground state lead to the formation of topological defects. The universality class of the transition imprints a signature on the resulting density of topological defects: It obeys a power law in the quench rate, with an exponent dictated by a combination of the critical exponents of the transition. In inhomogeneous systems the situation is more complicated, as the spontaneous symmetry breaking competes with bias caused by the influence of the nearby regions that already chose the new vacuum. As a result, the choice of the broken symmetry vacuum may be inherited from the neighboring regions that have already entered the new phase. This competition between the inherited and spontaneous symmetry breaking enhances the role of causality, as the defect formation is restricted to a fraction of the system where the front velocity surpasses the relevant sound velocity and phase transition remains effectively homogeneous. As a consequence, the overall number of topological defects can be substantially suppressed. When the fraction of the system is small, the resulting total number of defects is still given by a power law related to the universality class of the transition, but exhibits a more pronounced dependence on the quench rate. This enhanced dependence complicates the analysis but may also facilitate experimental test of defect formation theories.

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Quantum crystal growing: adiabatic preparation of a bosonic antiferromagnet in the presence of a parabolic inhomogeneity

Cited by 11 publications

References 71 publications

Dipoles on a two-leg ladder

Dipoles on a two-leg ladder

Adiabatic cooling of bosons in lattices to magnetically ordered quantum states

Causality and non-equilibrium second-order phase transitions in inhomogeneous systems

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