Pseudopotential treatment of two aligned dipoles under external harmonic confinement

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The low-energy scattering properties of two aligned identical bosonic and identical fermionic dipoles are analyzed. Generalized scattering lengths are determined as functions of the dipole moment and the scattering energy. Near resonance, where a new bound state is being pulled in, all non-vanishing generalized scattering lengths diverge, with the a 00 and a 11 scattering lengths being dominant for identical bosons and identical fermions, respectively, near both broad and narrow resonances. Implications for the energy spectrum and the eigenfunctions of trapped two-dipole systems and for pseudo-potential treatments are discussed. PACS numbers: 34.10.+x Currently, the creation of ultracold heteronuclear ground state molecules poses one of the major experimental challenges in the field of ultracold physics [1]. The trapping of ultracold ground state molecules with large phase space density promises to allow an exciting array of novel research lines to be studied. Although the largest phase space density of ultracold ground state molecules achieved to date is still fairly small, a number of promising cooling schemes have been demonstrated [2]. Thus, it is expected that degenerate molecular gases with large electric dipole moment will be created in the laboratory in the near future. Polar molecules are a candidate for qubits in quantum computing [3] and may be used in high precision measurements that aim at placing yet stricter limits on the electric dipole moment of the electron [4]. Furthermore, dipolar gases are predicted to show roton-like features [5] and to exhibit rich stability diagrams whose details depend on the trapping geometry [6]. The stability of dipolar atomic Cr condensates has recently been investigated experimentally. To enhance the anisotropic effects, which are due to Cr's magnetic dipole moment, the s-wave scattering length was tuned to zero by applying an external field in the vicinity of a Fano-Feshbach resonance [7].To create and then utilize ultracold molecules, it is mandatory to develop a detailed understanding of the scattering properties of two interacting dipoles in free space and in a trap. Unlike the interaction between s-wave alkali atoms, the interaction between two dipoles is long-range and angledependent. A two-dipole system can, e.g., be realized experimentally by loading an optical lattice with either two or zero dipoles per site. If the optical lattice is sufficiently deep and if the interaction between nearest and next to nearest neighbors are absent or negligible, then each optical lattice site can be treated as an independent approximately harmonic trap. This paper determines the scattering properties of two aligned dipoles, either identical bosons or identical fermions, as functions of the dipole moment and the scattering energy. In general, the dipoles can either be magnetic or electric. For concreteness, we restrict our discussion in the following to the scattering between molecular electric dipoles. Sequences of scattering resonances, which can be classified as "broad...

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confidence: 99%

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confidence: 99%

Low-energy resonances and bound states of aligned bosonic and fermionic dipoles

Kanjilal

Blume

2008

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“…Far from any scattering resonances the interaction can be represented by a pseudo-potential which includes the bare dipole-dipole interaction [4,5],…”

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confidence: 99%

Thomas-Fermi versus one- and two-dimensional regimes of a trapped dipolar Bose-Einstein condensate

Parker

O’Dell

2008

We derive the criteria for the Thomas-Fermi regime of a dipolar Bose-Einstein condensate in cigar, pancake and spherical geometries. This also naturally gives the criteria for the mean-field one-and two-dimensional regimes. Our predictions, including the Thomas-Fermi density profiles, are shown to be in excellent agreement with numerical solutions. Importantly, the anisotropy of the interactions has a profound effect on the Thomas-Fermi/low-dimensional criteria.PACS numbers: 03.75. Hh, 75.80.+q Introduction. A Bose-Einstein condensate (BEC) is said to be in the Thomas-Fermi (TF) regime when the interaction energy dominates the zero-point energy [1,2]. Despite being a dilute gas, in this regime the BEC is strongly affected by interactions and behaves in a highly non-ideal manner. Furthermore, the TF description is relatively simple compared to full Gross-Pitaevskii theory and facilitates exact results [1]. Consider a BEC containing N atoms of mass m confined to a spherical harmonic trap V (r) = mω 2 r 2 /2, with harmonic oscillator (HO) length l ho = /(mω), and repulsive s-wave interactions with positive scattering length a. The TF regime occurs for large values of the parameter N a/l ho , and thus typically arises for dense strongly repulsive BECs.Recently, a dipolar BEC was created with atomic dipoles polarized in a common direction by an external field [3]. Far from any scattering resonances the interaction can be represented by a pseudo-potential which includes the bare dipole-dipole interaction [4,5],

“…In the presence of the harmonic trap, k is determined, in a self-consistent manner, by the eigenenergies E rel 2 of Eq. (10) [31]. Since m is a good quantum number, each m-channel is treated by a m-specific pseudopotential; for details on the m = 0 case, see Ref.…”

Section: Virial Equation Of State and System Under Studymentioning

confidence: 99%

“…The model potential V model is characterized by two length scales, the hard wall radius (or short-range length) r c and the dipole length (or long-range length) D, D = µ red d 2 / 2 , where d denotes the dipole moment. In the second approach, we use the regularized zero-range pseudopotential V m pp,reg [29][30][31],…”

Section: Virial Equation Of State and System Under Studymentioning

confidence: 99%

Tunable high-temperature thermodynamics of weakly interacting dipolar gases

Daily

Blume

2014

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We consider dilute gases of dipolar bosons or fermions in the high-temperature limit in a spherically symmetric harmonic trapping potential. We examine the system using a virial expansion up to second order in the fugacity. Using the Born approximation and assuming purely dipolar interactions, we find that the second-order virial coefficient for both bosons and fermions depends quadratically on the dipole length and is negative at high temperature, indicating that to lowest order in the dipole-dipole interactions the dipolar single-component quantum gases are repulsive. If the s-wave scattering length for the bosonic system is tunable and its absolute value is made small, then the s-wave interactions dominate and the dipolar gas behaves like a weakly-interacting Bose gas with isotropic s-wave interactions. If the generalized scattering lengths for the fermionic system are tunable, then the dipole length can enter linearly in the virial equation of state, enhancing the dipole-dipole effects in the thermodynamic observables.