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Cold Bose Gases near Feshbach Resonances

Yeong E. Kim, Er L. Zubarev

Published Jan 1, 2002• 6 citations
OpenAlex

Abstract

(2002)] has been generalized for a dilute (in the sense that the range of interatomic potential, R, is small compared with inter-particle spacing r0) uniform gas of bosons near the Feshbach resonance using the multi-channel zero-range potential model. The method has been applied to Na(F = 1, mF = 1) atoms near the B0 = 907G Feshbach resonance. It is shown that at high densities na3 ≫ 1, there are significant differences between our results for the real part of energy per particle and the one-channel zero-range potential approximation. We point out the possibility of stabilization of the uniform condensate for the case of negative scattering length.

Related papers

Cold Bose Gases near Feshbach Resonances

Yeong E. Kim, Alexander L. Zubarev

The lowest order constrained variational method [Phys. Rev. Lett. 88, 210403 (2002)] has been generalized for a dilute (in the sense that the range of interatomic potential is small compared with inter-particle spacing) uniform gas of bosons near the Feshbach resonance using the multi-channel zero-range potential model. The method has been applied to Na (F=1, m_F=1) atoms near the $B_0=907$G Feshbach resonance. It is shown that at high densities, there are significant differences between our results for the real part of energy per particle and the one-channel zero-range potential approximation. We point out the possibility of stabilization of the uniform con densate for the case of negative scattering length.

arXiv:cond-mat/0305692•May 29, 2003•0 citations

Microscopic many-body theory of atomic Bose gases near a Feshbach resonance

R. A. Duine, Henk T. C. Stoof

A Feshbach resonance in the s-wave scattering length occurs if the energy of the two atoms in the incoming open channel is close to the energy of a bound state in a coupled closed channel. Starting from the microscopic Hamiltonian that describes this situation, we derive the effective atom–molecule theory for a Bose gas near a Feshbach resonance. In order to take into account all two-body processes, we have to dress the bare couplings of the atom–molecule model with ladder diagrams. This results in a quantum field theory that exactly reproduces the scattering amplitude of the atoms and the bound-state energy of the molecules. Since these properties are incorporated at the quantum level, the theory can be applied both above and below the critical temperature of the gas. Moreover, making use of the true interatomic potentials ensures that no divergences are encountered at any stage of the calculation. We also present the mean-field theory for the Bose–Einstein condensed phase of the gas.

arXiv:cond-mat/0210544•Journal of Optics B Quantum and Semiclassical Optics•Apr 1, 2003•49 citations

Bose-Einstein condensates in 85Rb gases at higher densities

Asaad R. Sakhel, Jonathan L. DuBois, H. R. Glyde

The Bose-Einstein condensation in trapped gases of ${}^{85}\mathrm{Rb}$ at densities beyond the dilute regime can now be realized taking advantage of Feshbach resonances. The gas density may be characterized by the parameter ${\mathrm{na}}^{3},$ where $n=N/V$ is the number density and a is the scattering length which is tuned using Feshbach resonance. We explore the properties of interacting trapped bosons in the density range $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}<~{\mathrm{na}}^{3}<~5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$ using Monte Carlo methods to compare with experiments. We find that there is a significant depletion of the condensate at $T=0\mathrm{K},$ for example, $25%$ at ${\mathrm{na}}^{3}{=10}^{\ensuremath{-}2}.$ The condensate is not concentrated at the center of the trap but is spread out over four or five trap lengths. The condensate density distributions and the total density distributions within the trap are very similar and the condensate fraction is $100%$ at the edges of the trap.

Physical Review A•Dec 31, 2002•11 citations

Nature of Bose gases near Feshbach resonance : the interplay between few-body and many-body physics

Mohammad Sadegh Mashayekhi

In this thesis, we investigated the physics of two- and three-dimensional ultra cold Bose gases in the strongly interacting regime at zero temperature. This regime can be experimentally accessed using a Feshbach resonance. We applied a self-consistent diagrammatic approach to determine the chemical potential of three-dimensional Bose gases for a wide range of interaction values. We showed that such strongly interacting Bose gases become unstable towards the formation of molecules at a finite positive scattering length. In fact, the interaction between atoms becomes effectively attractive and the system looses its metastability before reaching the unitary limit. We also found that such systems are nearly fermionized close to the instability point. Near this critical point, the chemical potential reaches a maximum and the contribution to the system energy due to three-body forces is estimated to be only a few percent. We also studied the same system using a self-consistent renormalization group method. This approach confirms the existence of an instability point towards the formation of molecules as well as fermionization. We showed that the instability and accompanying maximum are precursors of the sign change of the effective two-body interaction strength from repulsive to attractive near resonance. In addition, we examined the physics of two-dimensional Bose gases near resonance using a similar self-consistent diagrammatic approach as the one introduced for three-dimensional Bose gases. We demonstrated that a competition between three-body attractive interactions and two-body repulsive forces results in the chemical potential of two-dimensional Bose gases to exhibit a maximum at a critical scattering length beyond which these quantum gases possess a negative compressibility. For larger scattering lengths, the increasingly prominent role played by three-body attractive interactions leads to an onset instability at a second critical value. The three-body effects studied for these systems are universal, fully characterized by the effective two-dimensional scattering length and are, in comparison to the three-dimensional case, independent of three-body ultraviolet physics.

•Jan 1, 2014•0 citations

Observation of a Feshbach Resonance in Cold Atom Scattering

Daniel J. Heinzen, Ph. W. Courteille, R. S. Freeland

Due to atomic interactions, a dilute gas Bose-Einstein condensate acquires a self- energy proportional to the two-body scattering length a. This self-energy strongly influences the stability, formation rate, size and shape, collective excitations, and other properties of a condensate. For a given atomic species at zero magnetic field, the scattering length is fixed, and this had led to a rather limited range of interaction strengths in experiments. However, it has been predicted that a magnetically tunable Feshbach resonance could be used to strongly modify scattering lengths [1]. We have observed such a Feshbach resonance in collisions of ultracold 85Rb(f =2, mf=−2) atoms in a magnetic field B. From our measured resonance position and width, we infer that the scattering length a2,−2 for collisions of these atoms has the dispersive resonance form.

•May 3, 1998•0 citations

Behavior of trapped ultracold dilute Bose gases at large scattering length near a Feshbach resonance

M. L. Lekala, Barnali Chakrabarti, Gaotsiwe Joel Rampho +3 more

We calculate the ground-state energy and the collective excitation frequency of trapped bosons at large scattering length interacting via the realistic two-body van der Waals potential. Our many-body method keeps two-body correlations produced by all interacting pairs. When the scattering length is small compared to the trap size and the number of bosons in the trap is of the order of a few thousands, the mean-field results are in good agreement with the many-body results. However for large particle numbers, even when the condensate is sufficiently dilute, the interatomic correlation comes into the picture. When the scattering length is quite large near the Feshbach resonance, the Bose gas becomes highly correlated. The many-body results are close to the Gross-Pitaevskii results for a small number of bosons, however, large deviations are noted in the large particle limit. We also calculate the lowest collective excitation and the interaction energy for large scattering lengths. The monopole excitation frequency exhibits a pronounced dependence on the scattering length. We also observe a universal behavior for the interaction energy at the limit of large scattering length.

Physical Review A•Feb 18, 2014•10 citations
(2002)] has been generalized for a dilute (in the sense that the range of interatomic potential, R, is small compared with inter-particle spacing r0) uniform gas of bosons near the Feshbach resonance using the multi-channel zero-range potential model. The method has been applied to Na(F = 1, mF = 1) atoms near the B0 = 907G Feshbach resonance. It is shown that at high densities na3 ≫ 1, there are significant differences between our results for the real part of energy per particle and the one-channel zero-range potential approximation. We point out the possibility of stabilization of the uniform condensate for the case of negative scattering length.
The lowest order constrained variational method [Phys. Rev. Lett. 88, 210403 (2002)] has been generalized for a dilute (in the sense that the range of interatomic potential is small compared with inter-particle spacing) uniform gas of bosons near the Feshbach resonance using the multi-channel zero-range potential model. The method has been applied to Na (F=1, m_F=1) atoms near the B0=907B_0=907B0​=907G Feshbach resonance. It is shown that at high densities, there are significant differences between our results for the real part of energy per particle and the one-channel zero-range potential approximation. We point out the possibility of stabilization of the uniform con densate for the case of negative scattering length.
A Feshbach resonance in the s-wave scattering length occurs if the energy of the two atoms in the incoming open channel is close to the energy of a bound state in a coupled closed channel. Starting from the microscopic Hamiltonian that describes this situation, we derive the effective atom–molecule theory for a Bose gas near a Feshbach resonance. In order to take into account all two-body processes, we have to dress the bare couplings of the atom–molecule model with ladder diagrams. This results in a quantum field theory that exactly reproduces the scattering amplitude of the atoms and the bound-state energy of the molecules. Since these properties are incorporated at the quantum level, the theory can be applied both above and below the critical temperature of the gas. Moreover, making use of the true interatomic potentials ensures that no divergences are encountered at any stage of the calculation. We also present the mean-field theory for the Bose–Einstein condensed phase of the gas.
The Bose-Einstein condensation in trapped gases of 85Rb{}^{85}\mathrm{Rb}85Rb at densities beyond the dilute regime can now be realized taking advantage of Feshbach resonances. The gas density may be characterized by the parameter na3,{\mathrm{na}}^{3},na3, where n=N/Vn=N/Vn=N/V is the number density and a is the scattering length which is tuned using Feshbach resonance. We explore the properties of interacting trapped bosons in the density range $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}<~{\mathrm{na}}^{3}<~5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$ using Monte Carlo methods to compare with experiments. We find that there is a significant depletion of the condensate at T=0K,T=0\mathrm{K},T=0K, for example, 2525%25 at ${\mathrm{na}}^{3}{=10}^{\ensuremath{-}2}.$ The condensate is not concentrated at the center of the trap but is spread out over four or five trap lengths. The condensate density distributions and the total density distributions within the trap are very similar and the condensate fraction is 100100%100 at the edges of the trap.
In this thesis, we investigated the physics of two- and three-dimensional ultra cold Bose gases in the strongly interacting regime at zero temperature. This regime can be experimentally accessed using a Feshbach resonance. We applied a self-consistent diagrammatic approach to determine the chemical potential of three-dimensional Bose gases for a wide range of interaction values. We showed that such strongly interacting Bose gases become unstable towards the formation of molecules at a finite positive scattering length. In fact, the interaction between atoms becomes effectively attractive and the system looses its metastability before reaching the unitary limit. We also found that such systems are nearly fermionized close to the instability point. Near this critical point, the chemical potential reaches a maximum and the contribution to the system energy due to three-body forces is estimated to be only a few percent. We also studied the same system using a self-consistent renormalization group method. This approach confirms the existence of an instability point towards the formation of molecules as well as fermionization. We showed that the instability and accompanying maximum are precursors of the sign change of the effective two-body interaction strength from repulsive to attractive near resonance. In addition, we examined the physics of two-dimensional Bose gases near resonance using a similar self-consistent diagrammatic approach as the one introduced for three-dimensional Bose gases. We demonstrated that a competition between three-body attractive interactions and two-body repulsive forces results in the chemical potential of two-dimensional Bose gases to exhibit a maximum at a critical scattering length beyond which these quantum gases possess a negative compressibility. For larger scattering lengths, the increasingly prominent role played by three-body attractive interactions leads to an onset instability at a second critical value. The three-body effects studied for these systems are universal, fully characterized by the effective two-dimensional scattering length and are, in comparison to the three-dimensional case, independent of three-body ultraviolet physics.
Due to atomic interactions, a dilute gas Bose-Einstein condensate acquires a self- energy proportional to the two-body scattering length a. This self-energy strongly influences the stability, formation rate, size and shape, collective excitations, and other properties of a condensate. For a given atomic species at zero magnetic field, the scattering length is fixed, and this had led to a rather limited range of interaction strengths in experiments. However, it has been predicted that a magnetically tunable Feshbach resonance could be used to strongly modify scattering lengths [1]. We have observed such a Feshbach resonance in collisions of ultracold 85Rb(f =2, mf=−2) atoms in a magnetic field B. From our measured resonance position and width, we infer that the scattering length a2,−2 for collisions of these atoms has the dispersive resonance form.
We calculate the ground-state energy and the collective excitation frequency of trapped bosons at large scattering length interacting via the realistic two-body van der Waals potential. Our many-body method keeps two-body correlations produced by all interacting pairs. When the scattering length is small compared to the trap size and the number of bosons in the trap is of the order of a few thousands, the mean-field results are in good agreement with the many-body results. However for large particle numbers, even when the condensate is sufficiently dilute, the interatomic correlation comes into the picture. When the scattering length is quite large near the Feshbach resonance, the Bose gas becomes highly correlated. The many-body results are close to the Gross-Pitaevskii results for a small number of bosons, however, large deviations are noted in the large particle limit. We also calculate the lowest collective excitation and the interaction energy for large scattering lengths. The monopole excitation frequency exhibits a pronounced dependence on the scattering length. We also observe a universal behavior for the interaction energy at the limit of large scattering length.