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Deng F, Chen XY, Luo XY, Zhang W, Yi S, Shi T. Effective Potential and Superfluidity of Microwave-Shielded Polar Molecules. PHYSICAL REVIEW LETTERS 2023; 130:183001. [PMID: 37204905 DOI: 10.1103/physrevlett.130.183001] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/08/2022] [Revised: 03/08/2023] [Accepted: 04/09/2023] [Indexed: 05/21/2023]
Abstract
We analytically show that the effective interaction potential between microwave-shielded polar molecules consists of an anisotropic van der Waals-like shielding core and a modified dipolar interaction. This effective potential is validated by comparing its scattering cross sections with those calculated using intermolecular potential involving all interaction channels. It is shown that a scattering resonance can be induced under microwave fields reachable in current experiments. With the effective potential, we further study the Bardeen-Cooper-Schrieffer pairing in the microwave-shielded NaK gas. We show that the superfluid critical temperature is drastically enhanced near the resonance. As the effective potential is suitable for exploring the many-body physics of molecular gases, our results pave the way for studies of the ultracold gases of microwave-shielded molecular gases.
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Affiliation(s)
- Fulin Deng
- School of Physics and Technology, Wuhan University, Wuhan, Hubei 430072, China
- CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Xing-Yan Chen
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology, 80799 München, Germany
| | - Xin-Yu Luo
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology, 80799 München, Germany
| | - Wenxian Zhang
- School of Physics and Technology, Wuhan University, Wuhan, Hubei 430072, China
- Wuhan Institute of Quantum Technology, Wuhan, Hubei 430206, China
| | - Su Yi
- CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
- CAS Center for Excellence in Topological Quantum Computation and School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
- Peng Huanwu Collaborative Center for Research and Education, Beihang University, Beijing 100191, China
| | - Tao Shi
- CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
- CAS Center for Excellence in Topological Quantum Computation and School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
- Peng Huanwu Collaborative Center for Research and Education, Beihang University, Beijing 100191, China
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Kinnunen JJ, Baarsma JE, Martikainen JP, Törmä P. The Fulde-Ferrell-Larkin-Ovchinnikov state for ultracold fermions in lattice and harmonic potentials: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2018; 81:046401. [PMID: 29293087 DOI: 10.1088/1361-6633/aaa4ad] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We review the concepts and the present state of theoretical studies of spin-imbalanced superfluidity, in particular the elusive Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, in the context of ultracold quantum gases. The comprehensive presentation of the theoretical basis for the FFLO state that we provide is useful also for research on the interplay between magnetism and superconductivity in other physical systems. We focus on settings that have been predicted to be favourable for the FFLO state, such as optical lattices in various dimensions and spin-orbit coupled systems. These are also the most likely systems for near-future experimental observation of the FFLO state. Theoretical bounds, such as Bloch's and Luttinger's theorems, and experimentally important limitations, such as finite-size effects and trapping potentials, are considered. In addition, we provide a comprehensive review of the various ideas presented for the observation of the FFLO state. We conclude our review with an analysis of the open questions related to the FFLO state, such as its stability, superfluid density, collective modes and extending the FFLO superfluid concept to new types of lattice systems.
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Affiliation(s)
- Jami J Kinnunen
- COMP Center of Excellence, Department of Applied Physics, Aalto University, Fi-00076, Aalto, Finland
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3
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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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4
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Pototschnig JV, Hauser AW, Ernst WE. Electric dipole moments and chemical bonding of diatomic alkali-alkaline earth molecules. Phys Chem Chem Phys 2016; 18:5964-73. [PMID: 26837666 DOI: 10.1039/c5cp06598d] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
Abstract
We investigate the properties of alkali-alkaline earth diatomic molecules in the lowest Σ(+) states of the doublet and quartet multiplicity by ab initio calculations. In all sixteen cases studied, the permanent electric dipole moment points in opposite directions for the two spin states. This peculiarity can be explained by molecular orbital theory. We further discuss dissociation energies and bond distances. We analyze trends and provide an empirically motivated model for the prediction of the permanent electric dipole moment for combinations of alkali and alkaline earth atoms not studied in this work.
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Affiliation(s)
- Johann V Pototschnig
- Graz University of Technology, Institute of Experimental Physics, Petersgasse 16, 8010 Graz, Austria.
| | - Andreas W Hauser
- Graz University of Technology, Institute of Experimental Physics, Petersgasse 16, 8010 Graz, Austria.
| | - Wolfgang E Ernst
- Graz University of Technology, Institute of Experimental Physics, Petersgasse 16, 8010 Graz, Austria.
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Li Y, Wu C. Unconventional symmetries of Fermi liquid and Cooper pairing properties with electric and magnetic dipolar fermions. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2014; 26:493203. [PMID: 25401291 DOI: 10.1088/0953-8984/26/49/493203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
The rapid experimental progress of ultra-cold dipolar fermions opens up a whole new opportunity to investigate novel many-body physics of fermions. In this article, we review theoretical studies of the Fermi liquid theory and Cooper pairing instabilities of both electric and magnetic dipolar fermionic systems from the perspective of unconventional symmetries. When the electric dipole moments are aligned by the external electric field, their interactions exhibit the explicit d(r(2)-3z(2)) anisotropy. The Fermi liquid properties, including the single-particle spectra, thermodynamic susceptibilities and collective excitations, are all affected by this anisotropy. The electric dipolar interaction provides a mechanism for the unconventional spin triplet Cooper pairing, which is different from the usual spin-fluctuation mechanism in solids and the superfluid (3)He. Furthermore, the competition between pairing instabilities in the singlet and triplet channels gives rise to a novel time-reversal symmetry breaking superfluid state. Unlike electric dipole moments which are induced by electric fields and unquantized, magnetic dipole moments are intrinsic proportional to the hyperfine-spin operators with a Lande factor. Its effects even manifest in unpolarized systems exhibiting an isotropic but spin-orbit coupled nature. The resultant spin-orbit coupled Fermi liquid theory supports a collective sound mode exhibiting a topologically non-trivial spin distribution over the Fermi surface. It also leads to a novel p-wave spin triplet Cooper pairing state whose spin and orbital angular momentum are entangled to the total angular momentum J = 1 dubbed the J-triplet pairing. This J-triplet pairing phase is different from both the spin-orbit coupled (3)He-B phase with J = 0 and the spin-orbit decoupled (3)He-A phase.
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Affiliation(s)
- Yi Li
- Princeton Center for Theoretical Science, Princeton University, Princeton, NJ 08544, USA
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6
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Shi T, Zou SH, Hu H, Sun CP, Yi S. Ultracold fermi gases with resonant dipole-dipole interaction. PHYSICAL REVIEW LETTERS 2013; 110:045301. [PMID: 25166174 DOI: 10.1103/physrevlett.110.045301] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/11/2012] [Indexed: 06/03/2023]
Abstract
The superfluid phases in resonant dipolar Fermi gases are investigated by the standard mean-field theory. In contrast to the crossover from Bose-Einstein condensation (BEC) to Bardeen-Cooper-Schrieffer superfluid in Fermi gases with isotropic interactions, resonant dipolar interaction leads to two completely different BEC phases of the tight-binding Fermi molecules on both sides of the resonance, which are characterized by two order parameters with distinct internal symmetries. We point out that, near the resonances, the two competitive phases can coexist, and an emergent relative phase between the two order parameters spontaneously breaks time-reversal symmetry, which could be observed in momentum resolved rf spectroscopy.
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Affiliation(s)
- T Shi
- State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, P.O. Box 2735, Beijing 100190, China and Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany
| | - S-H Zou
- State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, P.O. Box 2735, Beijing 100190, China
| | - H Hu
- ARC Centre of Excellence for Quantum-Atom Optics, Centre for Atom Optics and Ultrafast Spectroscopy, Swinburne University of Technology, Melbourne 3122, Australia
| | - C-P Sun
- State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, P.O. Box 2735, Beijing 100190, China and Beijing Computational Science Research Center, Beijing 100084, China
| | - S Yi
- State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, P.O. Box 2735, Beijing 100190, China
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7
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The J-triplet Cooper pairing with magnetic dipolar interactions. Sci Rep 2012; 2:392. [PMID: 22550567 PMCID: PMC3340607 DOI: 10.1038/srep00392] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2011] [Accepted: 04/16/2012] [Indexed: 12/01/2022] Open
Abstract
Recently, cold atomic Fermi gases with the large magnetic dipolar interaction have been laser cooled down to quantum degeneracy. Different from electric-dipoles which are classic vectors, atomic magnetic dipoles are quantum-mechanical matrix operators proportional to the hyperfine-spin of atoms, thus provide rich opportunities to investigate exotic many-body physics. Furthermore, unlike anisotropic electric dipolar gases, unpolarized magnetic dipolar systems are isotropic under simultaneous spin-orbit rotation. These features give rise to a robust mechanism for a novel pairing symmetry: orbital p-wave (L = 1) spin triplet (S = 1) pairing with total angular momentum of the Cooper pair J = 1. This pairing is markedly different from both the 3He-B phase in which J = 0 and the 3He-A phase in which J is not conserved. It is also different from the p-wave pairing in the single-component electric dipolar systems in which the spin degree of freedom is frozen.
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Bhongale SG, Mathey L, Tsai SW, Clark CW, Zhao E. Bond order solid of two-dimensional dipolar fermions. PHYSICAL REVIEW LETTERS 2012; 108:145301. [PMID: 22540802 DOI: 10.1103/physrevlett.108.145301] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/09/2011] [Indexed: 05/31/2023]
Abstract
The recent experimental realization of dipolar Fermi gases near or below quantum degeneracy provides an opportunity to engineer Hubbard-like models with long-range interactions. Motivated by these experiments, we chart out the theoretical phase diagram of interacting dipolar fermions on the square lattice at zero temperature and half filling. We show that, in addition to p-wave superfluid and charge density wave order, two new and exotic types of bond order emerge generically in dipolar fermion systems. These phases feature homogeneous density but periodic modulations of the kinetic hopping energy between nearest or next-nearest neighbors. Similar, but manifestly different, phases of two-dimensional correlated electrons have previously only been hypothesized and termed "density waves of nonzero angular momentum." Our results suggest that these phases can be constructed flexibly with dipolar fermions, using currently available experimental techniques.
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Affiliation(s)
- S G Bhongale
- School of Physics, Astronomy and Computational Sciences, George Mason University, Fairfax, Virginia 22030, USA
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9
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Liu NN, Loesch H. Kinematic Slowing and Electrostatic Guiding of KBr Molecules Formed by the Reactive Collision Process: K + HBr → KBr + H. J Phys Chem A 2010; 114:3247-55. [DOI: 10.1021/jp909420n] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Ning-Ning Liu
- Fakultät für Physik, Universität Bielefeld, 33501 Bielefeld, Germany
| | - Hansjürgen Loesch
- Fakultät für Physik, Universität Bielefeld, 33501 Bielefeld, Germany
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10
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Nath R, Pedri P, Santos L. Phonon instability with respect to soliton formation in two-dimensional dipolar Bose-Einstein condensates. PHYSICAL REVIEW LETTERS 2009; 102:050401. [PMID: 19257488 DOI: 10.1103/physrevlett.102.050401] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/24/2008] [Revised: 11/25/2008] [Indexed: 05/27/2023]
Abstract
The partially attractive character of the dipole-dipole interaction leads to phonon instability in dipolar Bose-Einstein condensates, which is followed by collapse in 3D geometries. We show that in 2D, the nature of the post-instability dynamics is fundamentally different, due to the stabilization of 2D solitons. As a result, a transient gas of attractive solitons is formed, and collapse may be avoided. In the presence of an harmonic trap, the post-instability dynamics is characterized by a transient pattern formation followed by the creation of stable 2D solitons. This dynamics should be observable in ongoing experiments, allowing for the creation of stable 2D solitons for the first time ever in quantum gases.
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Affiliation(s)
- R Nath
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstr. 2, D-30167, Hannover, Germany
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11
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Bruun GM, Taylor E. Quantum phases of a two-dimensional dipolar fermi gas. PHYSICAL REVIEW LETTERS 2008; 101:245301. [PMID: 19113629 DOI: 10.1103/physrevlett.101.245301] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/08/2008] [Revised: 10/15/2008] [Indexed: 05/27/2023]
Abstract
We examine the superfluid and collapse instabilities of a quasi-two-dimensional gas of dipolar fermions aligned by an orientable external field. It is shown that the interplay between the anisotropy of the dipole-dipole interaction, the geometry of the system, and the p-wave symmetry of the superfluid order parameter means that the effective interaction for pairing can be made very large without the system collapsing. This leads to a broad region in the phase diagram where the system forms a stable superfluid. Analyzing the superfluid transition at finite temperatures, we calculate the Berezinskii-Kosterlitz-Thouless temperature as a function of the dipole angle.
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Affiliation(s)
- G M Bruun
- CNR-INFM BEC Center, Università di Trento, I-38050 Povo, Trento, Italy
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12
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Nath R, Pedri P, Santos L. Stability of dark solitons in three dimensional dipolar Bose-Einstein condensates. PHYSICAL REVIEW LETTERS 2008; 101:210402. [PMID: 19113395 DOI: 10.1103/physrevlett.101.210402] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2007] [Indexed: 05/27/2023]
Abstract
The dynamical stability of dark solitons in dipolar Bose-Einstein condensates is studied. For standard short-range interacting condensates, dark solitons are unstable against transverse excitations in two and three dimensions. On the contrary, due to its nonlocal character, the dipolar interaction allows for stable 3D stationary dark solitons, opening a qualitatively novel scenario in nonlinear atom optics. We discuss in detail the conditions to achieve this stability, which demand the use of an additional optical lattice, and the stability regimes.
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Affiliation(s)
- R Nath
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstr. 2, D-30167, Hannover, Germany
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13
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Klawunn M, Nath R, Pedri P, Santos L. Transverse instability of straight vortex lines in dipolar Bose-Einstein condensates. PHYSICAL REVIEW LETTERS 2008; 100:240403. [PMID: 18643556 DOI: 10.1103/physrevlett.100.240403] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/13/2007] [Indexed: 05/26/2023]
Abstract
The physics of vortex lines in dipolar condensates is studied. Because of the nonlocality of the dipolar interaction, the 3D character of the vortex plays a more important role in dipolar gases than in typical short-range interacting ones. In particular, the dipolar interaction significantly affects the stability of the transverse modes of the vortex line. Remarkably, in the presence of a periodic potential along the vortexline, the spectrum of transverse modes shows a rotonlike minimum, which eventually destabilizes the straight vortex when the BEC as a whole is still stable, opening the possibility for new scenarios for vortex-line configurations in dipolar gases.
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Affiliation(s)
- M Klawunn
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstr. 2, D-30167, Hannover, Germany
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Sinha S, Santos L. Cold dipolar gases in quasi-one-dimensional geometries. PHYSICAL REVIEW LETTERS 2007; 99:140406. [PMID: 17930653 DOI: 10.1103/physrevlett.99.140406] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/22/2007] [Indexed: 05/25/2023]
Abstract
We analyze the physics of cold dipolar gases in quasi-one-dimensional geometries, showing that the confinement-induced scattering resonances produced by the transversal trapping are crucially affected by the dipole-dipole interaction. As a consequence, the dipolar interaction may drastically change the properties of quasi-1D dipolar condensates, even for situations in which the dipolar interaction would be completely overwhelmed by the short-range interactions in a 3D environment.
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Affiliation(s)
- S Sinha
- S N Bose National Centre for Basic Sciences, Block JD, Sector III, Kolkata, India
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15
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Liu NN, Loesch H. Kinematic slowing of molecules formed by reactive collisions. PHYSICAL REVIEW LETTERS 2007; 98:103002. [PMID: 17358529 DOI: 10.1103/physrevlett.98.103002] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/18/2006] [Indexed: 05/14/2023]
Abstract
We report the generation of a beam of slow (translationally cold) KBr molecules formed by exoergic reactive collisions in counterpropagating beams of K atoms and HBr molecules. The intensity of the slow beam is estimated to 4x10(11) s-1 sr-1. The velocity distribution (density) peaks at 42.5 m/s corresponding to a formal temperature of 13 K. About 7% of the molecules move at velocities between 14.2 and 20 m/s and an estimated fraction of 7% is slower than 14.2 m/s.
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Affiliation(s)
- Ning-Ning Liu
- Fakultät für Physik, Universität Bielefeld, Universitätsstrasse 25, D-33615 Bielefeld, Germany
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Maussang K, Egorov D, Helton JS, Nguyen SV, Doyle JM. Zeeman relaxation of CaF in low-temperature collisions with helium. PHYSICAL REVIEW LETTERS 2005; 94:123002. [PMID: 15903915 DOI: 10.1103/physrevlett.94.123002] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/10/2004] [Indexed: 05/02/2023]
Abstract
The collision-induced Zeeman relaxation rate for collisions of CaF X2Sigma(v('')=0) with 3He is measured to be Gamma(Z)=(7.7+5.4/-2.5)x10(-15) cm(3)/s at 2 K. This rate is a direct measurement of the influence of spin-rotation coupling on Zeeman relaxation in the first rotational level of CaF. The relationship of this rate to known molecular constants is consistent with recent theory of cold molecular collisions and outlines the (2)Sigma molecules conducive to magnetic trapping.
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Affiliation(s)
- Kenneth Maussang
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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