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Bigagli N, Yuan W, Zhang S, Bulatovic B, Karman T, Stevenson I, Will S. Observation of Bose-Einstein condensation of dipolar molecules. Nature 2024:10.1038/s41586-024-07492-z. [PMID: 38831053 DOI: 10.1038/s41586-024-07492-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/18/2023] [Accepted: 04/30/2024] [Indexed: 06/05/2024]
Abstract
Ensembles of particles governed by quantum mechanical laws exhibit intriguing emergent behaviour. Atomic quantum gases1,2, liquid helium3,4 and electrons in quantum materials5-7 all exhibit distinct properties because of their composition and interactions. Quantum degenerate samples of ultracold dipolar molecules promise the realization of new phases of matter and new avenues for quantum simulation8 and quantum computation9. However, rapid losses10, even when reduced through collisional shielding techniques11-13, have so far prevented evaporative cooling to a Bose-Einstein condensate (BEC). Here we report on the realization of a BEC of dipolar molecules. By strongly suppressing two- and three-body losses via enhanced collisional shielding, we evaporatively cool sodium-caesium molecules to quantum degeneracy and cross the phase transition to a BEC. The BEC reveals itself by a bimodal distribution when the phase-space density exceeds 1. BECs with a condensate fraction of 60(10)% and a temperature of 6(2) nK are created and found to be stable with a lifetime close to 2 s. This work opens the door to the exploration of dipolar quantum matter in regimes that have been inaccessible so far, promising the creation of exotic dipolar droplets14, self-organized crystal phases15 and dipolar spin liquids in optical lattices16.
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Affiliation(s)
- Niccolò Bigagli
- Department of Physics, Columbia University, New York, NY, USA
| | - Weijun Yuan
- Department of Physics, Columbia University, New York, NY, USA
| | - Siwei Zhang
- Department of Physics, Columbia University, New York, NY, USA
| | - Boris Bulatovic
- Department of Physics, Columbia University, New York, NY, USA
| | - Tijs Karman
- Institute for Molecules and Materials, Radboud University, Nijmegen, The Netherlands
| | - Ian Stevenson
- Department of Physics, Columbia University, New York, NY, USA
| | - Sebastian Will
- Department of Physics, Columbia University, New York, NY, USA.
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2
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Adelhardt P, Koziol JA, Langheld A, Schmidt KP. Monte Carlo Based Techniques for Quantum Magnets with Long-Range Interactions. ENTROPY (BASEL, SWITZERLAND) 2024; 26:401. [PMID: 38785650 PMCID: PMC11120707 DOI: 10.3390/e26050401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/05/2024] [Revised: 04/17/2024] [Accepted: 04/19/2024] [Indexed: 05/25/2024]
Abstract
Long-range interactions are relevant for a large variety of quantum systems in quantum optics and condensed matter physics. In particular, the control of quantum-optical platforms promises to gain deep insights into quantum-critical properties induced by the long-range nature of interactions. From a theoretical perspective, long-range interactions are notoriously complicated to treat. Here, we give an overview of recent advancements to investigate quantum magnets with long-range interactions focusing on two techniques based on Monte Carlo integration. First, the method of perturbative continuous unitary transformations where classical Monte Carlo integration is applied within the embedding scheme of white graphs. This linked-cluster expansion allows extracting high-order series expansions of energies and observables in the thermodynamic limit. Second, stochastic series expansion quantum Monte Carlo integration enables calculations on large finite systems. Finite-size scaling can then be used to determine the physical properties of the infinite system. In recent years, both techniques have been applied successfully to one- and two-dimensional quantum magnets involving long-range Ising, XY, and Heisenberg interactions on various bipartite and non-bipartite lattices. Here, we summarise the obtained quantum-critical properties including critical exponents for all these systems in a coherent way. Further, we review how long-range interactions are used to study quantum phase transitions above the upper critical dimension and the scaling techniques to extract these quantum critical properties from the numerical calculations.
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Affiliation(s)
| | | | | | - Kai P. Schmidt
- Department of Physics, Friedrich-Alexander Universität Erlangen-Nürnberg (FAU), 91058 Erlangen, Germany; (P.A.); (J.A.K.); (A.L.)
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Nanoscale Phase Separation of Incommensurate and Quasi-Commensurate Spin Stripes in Low Temperature Spin Glass of La2−xSrxNiO4. CONDENSED MATTER 2021. [DOI: 10.3390/condmat6040045] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
While spin striped phases in La2−xSrxNiO4+y for 0.25 < x < 0.33 are the archetypal case of a 1D spin density wave (SDW) phase in doped antiferromagnetic strongly correlated perovskites, few information is available on the SDW spatial organization. In this context, we have measured the spatial variation of the wave vector of the SDW reflection profile by scanning micro X-ray diffractions with a coherent beam. We obtained evidence of a SDW order–disorder transition by lowering a high temperature phase (T > 50 K) to a low temperature phase (T < 50 K). We have identified quasi-commensurate spin stripe puddles in the ordered phase at 50 < T < 70 K, while the low temperature spin glassy phase presents a nanoscale phase separation of T = 30 K, with the coexistence of quasi-commensurate and incommensurate spin stripe puddles assigned to the interplay of quantum frustration and strong electronic correlations.
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4
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Böttcher F, Schmidt JN, Hertkorn J, Ng KSH, Graham SD, Guo M, Langen T, Pfau T. New states of matter with fine-tuned interactions: quantum droplets and dipolar supersolids. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2021; 84:012403. [PMID: 33176284 DOI: 10.1088/1361-6633/abc9ab] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/12/2023]
Abstract
Quantum fluctuations can stabilize Bose-Einstein condensates (BEC) against the mean-field collapse. Stabilization of the condensate has been observed in quantum degenerate Bose-Bose mixtures and dipolar BECs. The fine-tuning of the interatomic interactions can lead to the emergence of two new states of matter: liquid-like self-bound quantum droplets and supersolid crystals formed from these droplets. We review the properties of these exotic states of matter and summarize the experimental progress made using dipolar quantum gases and Bose-Bose mixtures. We conclude with an outline of important open questions that could be addressed in the future.
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Affiliation(s)
- Fabian Böttcher
- Physikalisches Institut and Center for Integrated Quantum Science and Technology, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
| | - Jan-Niklas Schmidt
- Physikalisches Institut and Center for Integrated Quantum Science and Technology, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
| | - Jens Hertkorn
- Physikalisches Institut and Center for Integrated Quantum Science and Technology, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
| | - Kevin S H Ng
- Physikalisches Institut and Center for Integrated Quantum Science and Technology, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
| | - Sean D Graham
- Physikalisches Institut and Center for Integrated Quantum Science and Technology, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
| | - Mingyang Guo
- Physikalisches Institut and Center for Integrated Quantum Science and Technology, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
| | - Tim Langen
- Physikalisches Institut and Center for Integrated Quantum Science and Technology, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
| | - Tilman Pfau
- Physikalisches Institut and Center for Integrated Quantum Science and Technology, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
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5
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Blackmore JA, Gregory PD, Bromley SL, Cornish SL. Coherent manipulation of the internal state of ultracold 87Rb 133Cs molecules with multiple microwave fields. Phys Chem Chem Phys 2020; 22:27529-27538. [PMID: 33079114 DOI: 10.1039/d0cp04651e] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We explore coherent multi-photon processes in 87Rb133Cs molecules using 3-level lambda and ladder configurations of rotational and hyperfine states, and discuss their relevance to future applications in quantum computation and quantum simulation. In the lambda configuration, we demonstrate the driving of population between two hyperfine levels of the rotational ground state via a two-photon Raman transition. Such pairs of states may be used in the future as a quantum memory, and we measure a Ramsey coherence time for a superposition of these states of 58(9) ms. In the ladder configuration, we show that we can generate and coherently populate microwave dressed states via the observation of an Autler-Townes doublet. We demonstrate that we can control the strength of this dressing by varying the intensity of the microwave coupling field. Finally, we perform spectroscopy of the rotational states of 87Rb133Cs up to N = 6, highlighting the potential of ultracold molecules for quantum simulation in synthetic dimensions. By fitting the measured transition frequencies we determine a new value of the centrifugal distortion coefficient Dv = h × 207.3(2) Hz.
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Affiliation(s)
- Jacob A Blackmore
- Joint Quantum Centre (JQC) Durham-Newcastle, Department of Physics, Durham University, South Road, Durham, DH1 3LE, UK.
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6
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Prestipino S. Ultracold Bosons on a Regular Spherical Mesh. ENTROPY (BASEL, SWITZERLAND) 2020; 22:E1289. [PMID: 33287057 PMCID: PMC7712534 DOI: 10.3390/e22111289] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/22/2020] [Revised: 11/08/2020] [Accepted: 11/11/2020] [Indexed: 11/19/2022]
Abstract
Here, the zero-temperature phase behavior of bosonic particles living on the nodes of a regular spherical mesh ("Platonic mesh") and interacting through an extended Bose-Hubbard Hamiltonian has been studied. Only the hard-core version of the model for two instances of Platonic mesh is considered here. Using the mean-field decoupling approximation, it is shown that the system may exist in various ground states, which can be regarded as analogs of gas, solid, supersolid, and superfluid. For one mesh, by comparing the theoretical results with the outcome of numerical diagonalization, I manage to uncover the signatures of diagonal and off-diagonal spatial orders in a finite quantum system.
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Affiliation(s)
- Santi Prestipino
- Dipartimento di Scienze Matematiche ed Informatiche, Scienze Fisiche e Scienze della Terra, Università degli Studi di Messina, Viale F. Stagno d'Alcontres 31, 98166 Messina, Italy
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7
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Masella G, Angelone A, Mezzacapo F, Pupillo G, Prokof'ev NV. Supersolid Stripe Crystal from Finite-Range Interactions on a Lattice. PHYSICAL REVIEW LETTERS 2019; 123:045301. [PMID: 31491241 DOI: 10.1103/physrevlett.123.045301] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/02/2018] [Revised: 05/21/2019] [Indexed: 06/10/2023]
Abstract
Strong, long-range interactions present a unique challenge for the theoretical investigation of quantum many-body lattice models, due to the generation of large numbers of competing states at low energy. Here, we investigate a class of extended bosonic Hubbard models with off-site terms interpolating between short and infinite range, thus allowing for an exact numerical solution for all interaction strengths. We predict a novel type of stripe crystal at strong coupling. Most interestingly, for intermediate interaction strengths we demonstrate that the stripes can turn superfluid, thus leading to a self-assembled array of quasi-one-dimensional superfluids. These bosonic superstripes turn into an isotropic supersolid with decreasing the interaction strength. The mechanism for stripe formation is based on cluster self-assembling in the corresponding classical ground state, reminiscent of classical soft-matter models of polymers, different from recently proposed mechanisms for cold gases of alkali or dipolar magnetic atoms.
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Affiliation(s)
- Guido Masella
- icFRC, IPCMS (UMR 7504) and ISIS (UMR 7006), Université de Strasbourg and CNRS, 67000 Strasbourg, France
| | - Adriano Angelone
- Abdus Salam International Centre for Theoretical Physics, strada Costiera 11, 34151 Trieste, Italy
- SISSA, via Bonomea 265, 34136 Trieste, Italy
| | - Fabio Mezzacapo
- icFRC, IPCMS (UMR 7504) and ISIS (UMR 7006), Université de Strasbourg and CNRS, 67000 Strasbourg, France
- Univ Lyon, Ens de Lyon, Univ Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France
| | - Guido Pupillo
- icFRC, IPCMS (UMR 7504) and ISIS (UMR 7006), Université de Strasbourg and CNRS, 67000 Strasbourg, France
| | - Nikolay V Prokof'ev
- icFRC, IPCMS (UMR 7504) and ISIS (UMR 7006), Université de Strasbourg and CNRS, 67000 Strasbourg, France
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
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8
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Abstract
We study the ground state phase diagram of a two dimensional mixed-spin system of coupled alternating spin-1 and 1/2 chains with a stripe supersolid phase. Utilizing different analytical and numerical approaches such as mean field approximation, cluster mean field theory and linear spin wave theory, we demonstrate that our system displays a rich ground state phase diagram including novel stripe supersolid, solids with different fillings and super-counterfluid phases, in addition to a stripe solid with half filling, superfluid and Mott insulating phases. In order to find a minimal mixed-spin model for stripe supersolidity, in the second part of the paper we consider two kinds of mixed-spin system of coupled alternating spin-1 and 1/2 chains with (i) anisotropic nearest neighbor interactions, (ii) anisotropic hoppings and study their ground state phase diagrams. We demonstrate that, for the systems with uniform hoppings, the repulsive intra-chains interactions are necessary for stripe supersolidity. In this case the minimal two dimensional mixed-spin model is a system of spin-1 and spin-1/2 XXZ chains, interacting via Ising Hamiltonian. In the case of anisotropic hoppings, a system of coupled Ising chains is the minimal model.
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9
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Liao R. Searching for Supersolidity in Ultracold Atomic Bose Condensates with Rashba Spin-Orbit Coupling. PHYSICAL REVIEW LETTERS 2018; 120:140403. [PMID: 29694153 DOI: 10.1103/physrevlett.120.140403] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/19/2017] [Indexed: 06/08/2023]
Abstract
We developed a functional integral formulation for the stripe phase of spinor Bose-Einstein condensates with Rashba spin-orbit coupling. The excitation spectrum is found to exhibit double gapless band structures, identified to be two Goldstone modes resulting from spontaneously broken internal gauge symmetry and translational invariance symmetry. The sound velocities display anisotropic behavior with the lower branch vanishing in the direction perpendicular to the stripe in the x-y plane. At the transition point between the plane-wave phase and the stripe phase, physical quantities such as fluctuation correction to the ground-state energy and quantum depletion of the condensates exhibit discontinuity, characteristic of the first-order phase transition. Despite strong quantum fluctuations induced by Rashba spin-orbit coupling, we show that the supersolid phase is stable against quantum depletion. Finally, we extend our formulation to finite temperatures to account for interactions between excitations.
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Affiliation(s)
- Renyuan Liao
- Fujian Provincial Key Laboratory for Quantum Manipulation and New Energy Materials, College of Physics and Energy, Fujian Normal University, Fuzhou 350117, China and Fujian Provincial Collaborative Innovation Center for Optoelectronic Semiconductors and Efficient Devices, Xiamen 361005, China
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10
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Abolins BP, Zillich RE, Whaley KB. Quantum phases of dipolar rotors on two-dimensional lattices. J Chem Phys 2018; 148:102338. [DOI: 10.1063/1.5005522] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022] Open
Affiliation(s)
- B. P. Abolins
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - R. E. Zillich
- Institut für Theoretische Physik, Johannes Kepler Universität Linz, Altenbergerstraße 69, 4040 Linz, Austria
| | - K. B. Whaley
- Department of Chemistry, University of California, Berkeley, California 94720, USA
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11
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Phonon-mediated repulsion, sharp transitions and (quasi)self-trapping in the extended Peierls-Hubbard model. Sci Rep 2017; 7:1169. [PMID: 28446754 PMCID: PMC5430795 DOI: 10.1038/s41598-017-01228-y] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/29/2016] [Accepted: 03/14/2017] [Indexed: 11/08/2022] Open
Abstract
We study two identical fermions, or two hard-core bosons, in an infinite chain and coupled to phonons by interactions that modulate their hopping as described by the Peierls/Su-Schrieffer-Heeger (SSH) model. We show that exchange of phonons generates effective nearest-neighbor repulsion between particles and also gives rise to interactions that move the pair as a whole. The two-polaron phase diagram exhibits two sharp transitions, leading to light dimers at strong coupling and the flattening of the dimer dispersion at some critical values of the parameters. This dimer (quasi)self-trapping occurs at coupling strengths where single polarons are mobile. This illustrates that, depending on the strength of the phonon-mediated interactions, the coupling to phonons may completely suppress or strongly enhance quantum transport of correlated particles.
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12
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Martin AM, Marchant NG, O'Dell DHJ, Parker NG. Vortices and vortex lattices in quantum ferrofluids. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:103004. [PMID: 28145899 DOI: 10.1088/1361-648x/aa53a6] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
The experimental realization of quantum-degenerate Bose gases made of atoms with sizeable magnetic dipole moments has created a new type of fluid, known as a quantum ferrofluid, which combines the extraordinary properties of superfluidity and ferrofluidity. A hallmark of superfluids is that they are constrained to rotate through vortices with quantized circulation. In quantum ferrofluids the long-range dipolar interactions add new ingredients by inducing magnetostriction and instabilities, and also affect the structural properties of vortices and vortex lattices. Here we give a review of the theory of vortices in dipolar Bose-Einstein condensates, exploring the interplay of magnetism with vorticity and contrasting this with the established behaviour in non-dipolar condensates. We cover single vortex solutions, including structure, energy and stability, vortex pairs, including interactions and dynamics, and also vortex lattices. Our discussion is founded on the mean-field theory provided by the dipolar Gross-Pitaevskii equation, ranging from analytic treatments based on the Thomas-Fermi (hydrodynamic) and variational approaches to full numerical simulations. Routes for generating vortices in dipolar condensates are discussed, with particular attention paid to rotating condensates, where surface instabilities drive the nucleation of vortices, and lead to the emergence of rich and varied vortex lattice structures. We also present an outlook, including potential extensions to degenerate Fermi gases, quantum Hall physics, toroidal systems and the Berezinskii-Kosterlitz-Thouless transition.
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Affiliation(s)
- A M Martin
- School of Physics, University of Melbourne, Victoria 3010, Australia
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13
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Baier S, Mark MJ, Petter D, Aikawa K, Chomaz L, Cai Z, Baranov M, Zoller P, Ferlaino F. Extended Bose-Hubbard models with ultracold magnetic atoms. Science 2016; 352:201-5. [DOI: 10.1126/science.aac9812] [Citation(s) in RCA: 201] [Impact Index Per Article: 25.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2015] [Accepted: 03/04/2016] [Indexed: 11/03/2022]
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14
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Angelone A, Mezzacapo F, Pupillo G. Superglass Phase of Interaction-Blockaded Gases on a Triangular Lattice. PHYSICAL REVIEW LETTERS 2016; 116:135303. [PMID: 27081986 DOI: 10.1103/physrevlett.116.135303] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/01/2015] [Indexed: 06/05/2023]
Abstract
We investigate the quantum phases of monodispersed bosonic gases confined to a triangular lattice and interacting via a class of soft-shoulder potentials. The latter correspond to soft-core potentials with an additional hard-core onsite interaction. Using exact quantum Monte Carlo simulations, we show that the low temperature phases for weak and strong interactions following a temperature quench are a homogeneous superfluid and a glass, respectively. The latter is an insulating phase characterized by inhomogeneity in the density distribution and structural disorder. Remarkably, we find that for intermediate interaction strengths a superglass occurs in an extended region of the phase diagram, where glassy behavior coexists with a sizable finite superfluid fraction. This glass phase is obtained in the absence of geometrical frustration or external disorder and is a result of the competition of quantum fluctuations and cluster formation in the corresponding classical ground state. For high enough temperature, the glass and superglass turn into a floating stripe solid and a supersolid, respectively. Given the simplicity and generality of the model, these phases should be directly relevant for state-of-the-art experiments with Rydberg-dressed atoms in optical lattices.
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Affiliation(s)
- Adriano Angelone
- icFRC, IPCMS (UMR 7504) and ISIS (UMR 7006), Université de Strasbourg and CNRS, 67000 Strasbourg, France
| | - Fabio Mezzacapo
- icFRC, IPCMS (UMR 7504) and ISIS (UMR 7006), Université de Strasbourg and CNRS, 67000 Strasbourg, France
| | - Guido Pupillo
- icFRC, IPCMS (UMR 7504) and ISIS (UMR 7006), Université de Strasbourg and CNRS, 67000 Strasbourg, France
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15
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Díaz-Méndez R, Mezzacapo F, Cinti F, Lechner W, Pupillo G. Monodisperse cluster crystals: Classical and quantum dynamics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:052307. [PMID: 26651695 DOI: 10.1103/physreve.92.052307] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/26/2015] [Indexed: 06/05/2023]
Abstract
We study the phases and dynamics of a gas of monodisperse particles interacting via soft-core potentials in two spatial dimensions, which is of interest for soft-matter colloidal systems and quantum atomic gases. Using exact theoretical methods, we demonstrate that the equilibrium low-temperature classical phase simultaneously breaks continuous translational symmetry and dynamic space-time homogeneity, whose absence is usually associated with out-of-equilibrium glassy phenomena. This results in an exotic self-assembled cluster crystal with coexisting liquidlike long-time dynamical properties, which corresponds to a classical analog of supersolid behavior. We demonstrate that the effects of quantum fluctuations and bosonic statistics on cluster-glassy crystals are separate and competing: Zero-point motion tends to destabilize crystalline order, which can be restored by bosonic statistics.
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Affiliation(s)
- Rogelio Díaz-Méndez
- IPCMS (UMR 7504) and ISIS (UMR 7006), Université de Strasbourg and CNRS, 67000 Strasbourg, France
| | - Fabio Mezzacapo
- IPCMS (UMR 7504) and ISIS (UMR 7006), Université de Strasbourg and CNRS, 67000 Strasbourg, France
| | - Fabio Cinti
- National Institute for Theoretical Physics, Stellenbosch 7600, South Africa
| | - Wolfgang Lechner
- IQOQI and Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck, Austria
| | - Guido Pupillo
- IPCMS (UMR 7504) and ISIS (UMR 7006), Université de Strasbourg and CNRS, 67000 Strasbourg, France
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16
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Yamamoto D, Marmorini G, Danshita I. Quantum phase diagram of the triangular-lattice XXZ model in a magnetic field. PHYSICAL REVIEW LETTERS 2014; 112:127203. [PMID: 24724677 DOI: 10.1103/physrevlett.112.127203] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/03/2013] [Indexed: 06/03/2023]
Abstract
The triangular lattice of S=1/2 spins with XXZ anisotropy is a ubiquitous model for various frustrated systems in different contexts. We determine the quantum phase diagram of the model in the plane of the anisotropy parameter and the magnetic field by means of a large-size cluster mean-field method with a scaling scheme. We find that quantum fluctuations break up the nontrivial continuous degeneracy into two first-order phase transitions. In between the two transition boundaries, the degeneracy-lifting results in the emergence of a new coplanar phase not predicted in the classical counterpart of the model. We suggest that the quantum phase transition to the nonclassical coplanar state can be observed in triangular-lattice antiferromagnets with large easy-plane anisotropy or in the corresponding optical-lattice systems.
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Affiliation(s)
- Daisuke Yamamoto
- Condensed Matter Theory Laboratory, RIKEN, Saitama 351-0198, Japan
| | - Giacomo Marmorini
- Condensed Matter Theory Laboratory, RIKEN, Saitama 351-0198, Japan and Research and Education Center for Natural Sciences, Keio University, Kanagawa 223-8521, Japan
| | - Ippei Danshita
- Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan and Computational Condensed Matter Physics Laboratory, RIKEN, Saitama 351-0198, Japan
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17
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Affiliation(s)
- Mikhail Lemeshko
- a ITAMP, Harvard-Smithsonian Center for Astrophysics , Cambridge , MA , 02138 , USA
- b Physics Department , Harvard University , Cambridge , MA , 02138 , USA
- c Kavli Institute for Theoretical Physics , University of California , Santa Barbara , CA , 93106 , USA
| | - Roman V. Krems
- c Kavli Institute for Theoretical Physics , University of California , Santa Barbara , CA , 93106 , USA
- d Department of Chemistry , University of British Columbia , BC V6T 1Z1, Vancouver , Canada
| | - John M. Doyle
- b Physics Department , Harvard University , Cambridge , MA , 02138 , USA
| | - Sabre Kais
- e Departments of Chemistry and Physics , Purdue University , West Lafayette , IN , 47907 , USA
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18
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Batrouni GG, Scalettar RT, Rousseau VG, Grémaud B. Competing supersolid and Haldane insulator phases in the extended one-dimensional bosonic Hubbard model. PHYSICAL REVIEW LETTERS 2013; 110:265303. [PMID: 23848892 DOI: 10.1103/physrevlett.110.265303] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/15/2013] [Indexed: 06/02/2023]
Abstract
The Haldane insulator is a gapped phase characterized by an exotic nonlocal order parameter. The parameter regimes at which it might exist, and how it competes with alternate types of order, such as supersolid order, are still incompletely understood. Using the stochastic Green function quantum Monte Carlo algorithm and density matrix renormalization group, we study numerically the ground state phase diagram of the one-dimensional bosonic Hubbard model with contact and near neighbor repulsive interactions. We show that, depending on the ratio of the near neighbor to contact interactions, this model exhibits charge density waves, superfluid, supersolid, and the recently identified Haldane insulating phases. We show that the Haldane insulating phase exists only at the tip of the unit-filling charge density wave lobe and that there is a stable supersolid phase over a very wide range of parameters.
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Affiliation(s)
- G G Batrouni
- INLN, Université de Nice-Sophia Antipolis, CNRS, 1361 route des Lucioles, 06560 Valbonne, France
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19
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Li Y, Martone GI, Pitaevskii LP, Stringari S. Superstripes and the excitation spectrum of a spin-orbit-coupled Bose-Einstein condensate. PHYSICAL REVIEW LETTERS 2013; 110:235302. [PMID: 25167508 DOI: 10.1103/physrevlett.110.235302] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/27/2013] [Revised: 04/23/2013] [Indexed: 06/03/2023]
Abstract
Using Bogoliubov theory we calculate the excitation spectrum of a spinor Bose-Einstein condensed gas with an equal Rashba and Dresselhaus spin-orbit coupling in the stripe phase. The emergence of a double gapless band structure is pointed out as a key signature of Bose-Einstein condensation and of the spontaneous breaking of translational invariance symmetry. In the long wavelength limit the lower and upper branches exhibit, respectively, a clear spin and density nature. For wave vectors close to the first Brillouin zone, the lower branch acquires an important density character responsible for the divergent behavior of the structure factor and of the static response function, reflecting the occurrence of crystalline order. The sound velocities are calculated as functions of the Raman coupling for excitations propagating orthogonal and parallel to the stripes. Our predictions provide new perspectives for the identification of supersolid phenomena in ultracold atomic gases.
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Affiliation(s)
- Yun Li
- INO-CNR BEC Center and Dipartimento di Fisica, Università di Trento, 38123 Povo, Italy
| | - Giovanni I Martone
- INO-CNR BEC Center and Dipartimento di Fisica, Università di Trento, 38123 Povo, Italy
| | - Lev P Pitaevskii
- INO-CNR BEC Center and Dipartimento di Fisica, Università di Trento, 38123 Povo, Italy and Kapitza Institute for Physical Problems, RAS, Kosygina 2, 119334 Moscow, Russia
| | - Sandro Stringari
- INO-CNR BEC Center and Dipartimento di Fisica, Università di Trento, 38123 Povo, Italy
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20
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Anders P, Werner P, Troyer M, Sigrist M, Pollet L. From the Cooper problem to canted supersolids in Bose-Fermi mixtures. PHYSICAL REVIEW LETTERS 2012; 109:206401. [PMID: 23215511 DOI: 10.1103/physrevlett.109.206401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/28/2012] [Indexed: 06/01/2023]
Abstract
We calculate the phase diagram of the Bose-Fermi Hubbard model on the 3d cubic lattice at fermionic half filling and bosonic unit filling by means of single-site dynamical mean-field theory. For fast bosons, this is equivalent to the Cooper problem in which the bosons can induce s-wave pairing between the fermions. We also find miscible superfluid and canted supersolid phases depending on the interspecies coupling strength. In contrast, slow bosons favor fermionic charge density wave structures for attractive fermionic interactions. These competing instabilities lead to a rich phase diagram within reach of cold gas experiments.
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Affiliation(s)
- Peter Anders
- Theoretische Physik, ETH Zurich, 8093 Zurich, Switzerland
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21
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Baranov MA, Dalmonte M, Pupillo G, Zoller P. Condensed Matter Theory of Dipolar Quantum Gases. Chem Rev 2012; 112:5012-61. [DOI: 10.1021/cr2003568] [Citation(s) in RCA: 480] [Impact Index Per Article: 40.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- M. A. Baranov
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck, Austria
- Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria
- RRC “Kurchatov Institute”,
Kurchatov Square 1, 123182, Moscow, Russia
| | - M. Dalmonte
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck, Austria
- Dipartimento di Fisica dell’Università
di Bologna, via Irnerio 46, 40126 Bologna, Italy
| | - G. Pupillo
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck, Austria
- Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria
- ISIS (UMR 7006) and IPCMS (UMR
7504), Université de Strasbourg and CNRS, Strasbourg, France
| | - P. Zoller
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck, Austria
- Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria
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22
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Peter D, Müller S, Wessel S, Büchler HP. Anomalous behavior of spin systems with dipolar interactions. PHYSICAL REVIEW LETTERS 2012; 109:025303. [PMID: 23030175 DOI: 10.1103/physrevlett.109.025303] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/07/2012] [Indexed: 06/01/2023]
Abstract
We study the properties of spin systems realized by cold polar molecules interacting via dipole-dipole interactions in two dimensions. Using a spin wave theory, that allows for the full treatment of the characteristic long-distance tail of the dipolar interaction, we find several anomalous features in the ground state correlations and the spin wave excitation spectrum, which are absent in their counterparts with short-range interaction. The most striking consequence is the existence of true long-range order at finite temperature for a two-dimensional phase with a broken U(1) symmetry.
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Affiliation(s)
- D Peter
- Institute for Theoretical Physics III, University of Stuttgart, Stuttgart, Germany
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23
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Henkel N, Cinti F, Jain P, Pupillo G, Pohl T. Supersolid vortex crystals in Rydberg-dressed Bose-Einstein condensates. PHYSICAL REVIEW LETTERS 2012; 108:265301. [PMID: 23004994 DOI: 10.1103/physrevlett.108.265301] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/24/2011] [Indexed: 06/01/2023]
Abstract
We study rotating quasi-two-dimensional Bose-Einstein condensates, in which atoms are dressed to a highly excited Rydberg state. This leads to weak effective interactions that induce a transition to a mesoscopic supersolid state. Considering slow rotation, we determine its superfluidity using quantum Monte Carlo simulations as well as mean field calculations. For rapid rotation, the latter reveal an interesting competition between the supersolid crystal structure and the rotation-induced vortex lattice that gives rise to new phases, including arrays of mesoscopic vortex crystals.
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Affiliation(s)
- N Henkel
- Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany
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24
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Ohgoe T, Suzuki T, Kawashima N. Commensurate supersolid of three-dimensional lattice bosons. PHYSICAL REVIEW LETTERS 2012; 108:185302. [PMID: 22681086 DOI: 10.1103/physrevlett.108.185302] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/27/2011] [Indexed: 06/01/2023]
Abstract
Using an unbiased quantum Monte Carlo method, we obtain convincing evidence of the existence of a checkerboard supersolid at a commensurate filling factor 1/2 (a commensurate supersolid) in the soft-core Bose-Hubbard model with nearest-neighbor repulsions on a cubic lattice. In conventional cases, supersolids are realized at incommensurate filling factors by a doped-defect-condensation mechanism, where particles (holes) doped into a perfect crystal act as interstitials (vacancies) and delocalize in the crystal order. However, in the model, a supersolid state is stabilized even at the commensurate filling factor 1/2 without doping. By performing grand canonical simulations, we obtain a ground-state phase diagram that suggests the existence of a supersolid at a commensurate filling. To obtain direct evidence of the commensurate supersolid, we next perform simulations in canonical ensembles at a particle density ρ=1/2 and exclude the possibility of phase separation. From the obtained snapshots, we discuss its microscopic structure and observe that interstitial-vacancy pairs are unbound in the crystal order.
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Affiliation(s)
- Takahiro Ohgoe
- Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan
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26
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Lu M, Burdick NQ, Youn SH, Lev BL. Strongly dipolar Bose-Einstein condensate of dysprosium. PHYSICAL REVIEW LETTERS 2011; 107:190401. [PMID: 22181585 DOI: 10.1103/physrevlett.107.190401] [Citation(s) in RCA: 112] [Impact Index Per Article: 8.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/30/2011] [Indexed: 05/31/2023]
Abstract
We report the Bose-Einstein condensation (BEC) of the most magnetic element, dysprosium. The Dy BEC is the first for an open f-shell lanthanide (rare-earth) element and is produced via forced evaporation in a crossed optical dipole trap loaded by an unusual, blue-detuned and spin-polarized narrowline magneto-optical trap. Nearly pure condensates of 1.5 × 10(4) (164)Dy atoms form below T = 30 nK. We observe that stable BEC formation depends on the relative angle of a small polarizing magnetic field to the axis of the oblate trap, a property of trapped condensates only expected in the strongly dipolar regime. This regime was heretofore only attainable in Cr BECs via a Feshbach resonance accessed at a high-magnetic field.
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Affiliation(s)
- Mingwu Lu
- Department of Applied Physics, Stanford University, Stanford, California 94305, USA
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27
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Zillich RE, Whaley KB. Homogeneous Bose gas of dipolar molecules in the mean field approximation. Phys Chem Chem Phys 2011; 13:18835-43. [DOI: 10.1039/c1cp21331h] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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28
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Debatin M, Takekoshi T, Rameshan R, Reichsöllner L, Ferlaino F, Grimm R, Vexiau R, Bouloufa N, Dulieu O, Nägerl HC. Molecular spectroscopy for ground-state transfer of ultracold RbCs molecules. Phys Chem Chem Phys 2011; 13:18926-35. [DOI: 10.1039/c1cp21769k] [Citation(s) in RCA: 63] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Affiliation(s)
- Markus Debatin
- Institut für Experimentalphysik und Zentrum für Quantenphysik, Universität Innsbruck, Technikerstrasse 25, A-6020 Innsbruck, Austria
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29
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Ni KK, Ospelkaus S, Wang D, Quéméner G, Neyenhuis B, de Miranda MHG, Bohn JL, Ye J, Jin DS. Dipolar collisions of polar molecules in the quantum regime. Nature 2010; 464:1324-8. [PMID: 20428166 DOI: 10.1038/nature08953] [Citation(s) in RCA: 174] [Impact Index Per Article: 12.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/15/2010] [Accepted: 02/23/2010] [Indexed: 11/09/2022]
Abstract
Ultracold polar molecules offer the possibility of exploring quantum gases with interparticle interactions that are strong, long-range and spatially anisotropic. This is in stark contrast to the much studied dilute gases of ultracold atoms, which have isotropic and extremely short-range (or 'contact') interactions. Furthermore, the large electric dipole moment of polar molecules can be tuned using an external electric field; this has a range of applications such as the control of ultracold chemical reactions, the design of a platform for quantum information processing and the realization of novel quantum many-body systems. Despite intense experimental efforts aimed at observing the influence of dipoles on ultracold molecules, only recently have sufficiently high densities been achieved. Here we report the experimental observation of dipolar collisions in an ultracold molecular gas prepared close to quantum degeneracy. For modest values of an applied electric field, we observe a pronounced increase in the loss rate of fermionic potassium-rubidium molecules due to ultracold chemical reactions. We find that the loss rate has a steep power-law dependence on the induced electric dipole moment, and we show that this dependence can be understood in a relatively simple model based on quantum threshold laws for the scattering of fermionic polar molecules. In addition, we directly observe the spatial anisotropy of the dipolar interaction through measurements of the thermodynamics of the dipolar gas. These results demonstrate how the long-range dipolar interaction can be used for electric-field control of chemical reaction rates in an ultracold gas of polar molecules. Furthermore, the large loss rates in an applied electric field suggest that creating a long-lived ensemble of ultracold polar molecules may require confinement in a two-dimensional trap geometry to suppress the influence of the attractive, 'head-to-tail', dipolar interactions.
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Affiliation(s)
- K-K Ni
- JILA, NIST and University of Colorado, Department of Physics, University of Colorado, Boulder, Colorado 80309-0440, USA
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30
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Capogrosso-Sansone B, Trefzger C, Lewenstein M, Zoller P, Pupillo G. Quantum phases of cold polar molecules in 2D optical lattices. PHYSICAL REVIEW LETTERS 2010; 104:125301. [PMID: 20366541 DOI: 10.1103/physrevlett.104.125301] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2009] [Revised: 02/22/2010] [Indexed: 05/29/2023]
Abstract
We study the quantum phases of hard-core bosonic polar molecules on a two-dimensional square lattice interacting via repulsive dipole-dipole interactions. In the limit of small tunneling, we find evidence for a devil's staircase, where Mott solids appear at rational fillings of the lattice. For finite tunneling, we establish the existence of extended regions of parameters where the ground state is a supersolid, obtained by doping the solids either with particles or vacancies. We discuss the effects of finite temperature and finite-size confining potentials as relevant to experiments.
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Affiliation(s)
- B Capogrosso-Sansone
- ITAMP, Harvard-Smithsonian Center of Astrophysics, Cambridge, Massachusetts 02138, USA
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