In this letter we consider dipolar quantum gases in a quasi-one-dimensional tube with dipole moment perpendicular to the tube direction. We deduce the effective one-dimensional interaction potential and show that this potential is not purely repulsive, but rather has an attractive part due to high-order scattering processes through transverse excited states. The attractive part can induce bound state and cause scattering resonances. This represents the dipole induced resonance in low-dimension. We work out an unconventional behavior of low-energy phase shift for this effective potential and show how it evolves across a resonance. Based on the phase shift, the interaction energy of spinless bosons is obtained using asymptotic Bethe ansatz. Despite of long-range nature of dipolar interaction, we find that a behavior similar as short-range Lieb-Linger gas emerges at the resonance regime.
We study strong interaction effects in a one-dimensional (1D) Boson gas across a narrow confinement induced resonance (CIR). In contrast to the zero range potential, the 1D two-body interaction in the narrow CIR can be written as a polynomial of derivative $delta$-function interaction on many-body level. Using the asymptotic Bethe ansatz, we find that the low energy physics of this many-body problem is described by the Tomonaga-Luttinger liquid where the Luttinger parameters are essentially modified by an effective finite range parameter $v$. This parameter drastically alters quantum criticality and universal thermodynamics of the gas. In particular, it drives the Tonks-Girardeau (TG) gas from non-mutual Fermi statistics to mutual statistics or to a more exclusive super TG gas. This novel feature is further discussed in terms of the breathing mode which is experimentally measurable.
It is known from the solution of the two-body problem that an anisotropic dipolar interaction can give rise to s-wave scattering resonances, which are named as dipolar interaction induced resonaces (DIIR). In this letter, we study zero-temperature many-body physics of a two-component Fermi gas across a DIIR. In the low-density regime, it is very striking that the resulting pairing order parameter is a nearly isotropic singlet pairing and the physics can be well described by an s-wave resonant interaction potential with finite range corrections, despite of the anisotropic nature of dipolar interaction. The pairing energy is as strong as a unitary Fermi gas nearby a magnetic Feshbach resonance. In the high density regime, the anisotropic effect plays an important role. We find phase transitions from singlet pairing to a state with mixed singlet and triplet pairing, and then from mixed pairing to pure triplet pairing. The state with mixed pairing spontaneously breaks the time-reversal symmetry.
We address the phase of a highly polarized Fermi gas across a narrow Feshbach resonance starting from the problem of a single down spin fermion immersed in a Fermi sea of up spins. Both polaron and pairing states are considered using the variational wave function approach, and we find that the polaron to pairing transition will take place at the BCS side of the resonance, strongly in contrast to a wide resonance where the transition is located at the BEC side. For pairing phase, we find out the critical strength of repulsive interaction between pairs above which the mixture of pairs and fermions will not phase separate. Therefore, nearby a narrow resonance, it is quite likely that magnetism can coexist with s-wave BCS superfluidity at large Zeeman field, which is a remarkable property absent in conventional BCS superconductors (or fermion pair superfluids).
We show that s-wave scattering resonances induced by dipolar interactions in a polar molecular gas have a universal large and positive effective range, which is very different from Feshbach resonances realized in cold atoms before, where the effective range is either negligible or negative. Such a difference has important consequence in many-body physics. At high temperature regime, a positive effective range gives rise to stronger repulsive interaction energy for positive scattering length, and weaker attractive interaction energy for negative scattering length. While at low-temperatures, we study polaron problem formed by single impurity molecule, and we find that the polaron binding energy increases at the BEC side and decreases at the BCS side. All these effects are in opposite to narrow Feshbach resonances where the effective range is negative.
We study the two-body problem with a spatially modulated interaction potential using a two-channel model, in which the inter-channel coupling is provided by an optical standing wave and its strength modulates periodically in space. As the modulation amplitudes increases, there will appear a sequence of bound states. Part of them will cause divergence of the effective scattering length, defined through the phase shift in the asymptotic behavior of scattering states. We also discuss how the local scattering length, defined through short-range behavior of scattering states, modulates spatially in different regimes. These results provide a theoretical guideline for new control technique in cold atom toolbox, in particular, for alkali-earth-(like) atoms where the inelastic loss is small.
We investigate the non-Abelian Josephson effect in spinor Bose-Einstein condensates with double optical traps. We propose, for the first time, a real physical system which contains non-Abelian Josephson effects. The collective modes of this weak coupling system have very different density and spin tunneling characters comparing to the Abelian case. We calculate the frequencies of the pseudo Goldstone modes in different phases between two traps respectively, which are a crucial feature of the non-Abelian Josephson effects. We also give an experimental protocol to observe this novel effect in future experiments.
We discuss a Casimir force due to zero-temperature quantum fluctuations in a weakly interacting Bose-Einstein condensate (BEC) with a strong harmonic trap. The results show that the presence of a strong harmonic trap changes the power law behavior of Casimir force due to the dimensional reduction effect. At finite temperature, we calculate Casimir force due to thermal fluctuation and find an exotic temperature dependent behavior in the first order term. Finally, we speculate some possible experimental realization and detection of the force in future experiments.
