Adiabatic passage through a Feshbach resonance in a degenerate quantum gas

Band, Yehuda B.; Tikhonenkov, I.; Pazy, E.; Fleischhauer, Michael; Vardi, Amichay

doi:10.1080/09500340600777771

Cited by 4 publications

(9 citation statements)

References 20 publications

(53 reference statements)

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“…II, but are valid for arbitrary direction of E. These equations correspond to a mean-field theory treatment obtained by taking the expectation values of Eqs. (13) and (14), replacing the expectation value of the productL ×n by the product of the expectation values [12][13][14][15] and taking the limit as → 0 on the RHS of (13).…”

Section: B Mean-field Dynamicsmentioning

confidence: 99%

Dynamics of an electric dipole moment in a stochastic electric field

Band

2013

Phys. Rev. E

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The mean-field dynamics of an electric dipole moment in a deterministic and a fluctuating electric field is solved to obtain the average over fluctuations of the dipole moment and the angular momentum as a function of time for a Gaussian white noise stochastic electric field. The components of the average electric dipole moment and the average angular momentum along the deterministic electric field direction do not decay to zero, despite fluctuations in all three components of the electric field. This is in contrast to the decay of the average over fluctuations of a magnetic moment in a stochastic magnetic field with Gaussian white noise in all three components. The components of the average electric dipole moment and the average angular momentum perpendicular to the deterministic electric field direction oscillate with time but decay to zero, and their variance grows with time.

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Section: B Mean-field Dynamicsmentioning

confidence: 99%

Dynamics of an electric dipole moment in a stochastic electric field

Band

2013

Phys. Rev. E

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“…II, and are valid for arbitrary direction of E. The mean-field theory treatment takes the expectation values of Eqs. (9) and (10), replacing the expectation value of the productL ×n by the product of the expectation values [10,11,13,14] and taking the limit as → 0 on the RHS of (9):…”

Section: A Mean-field Dynamicsmentioning

confidence: 99%

Molecules with an induced dipole moment in a stochastic electric field

Band

Ben-Shimol

2013

Phys. Rev. E

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The mean-field dynamics of a molecule with an induced dipole moment (e.g., a homonuclear diatomic molecule) in a deterministic and a stochastic (fluctuating) electric field is solved to obtain the decoherence properties of the system. The average (over fluctuations) electric dipole moment and average angular momentum as a function of time for a Gaussian white noise electric field are determined via perturbative and nonperturbative solutions in the fluctuating field. In the perturbative solution, the components of the average electric dipole moment and the average angular momentum along the deterministic electric field direction do not decay to zero, despite fluctuations in all three components of the electric field. This is in contrast to the decay of the average over fluctuations of a magnetic moment in a stochastic magnetic field with a Gaussian white noise magnetic field in all three components. In the nonperturbative solution, the component of the average electric dipole moment and the average angular momentum in the deterministic electric field direction also decay to zero.

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“…Though the numerical works of this category displayed a reasonable temperature dependence, they could not give a clear physical picture and detailed dependencies on parameters of the problem. The series of semi-analytical works by Pazy et al [22,25,26,27] were based on two contradicting assumptions as we show later.In this letter we consider the process of molecule production from fermi-gas of atoms after the FR is swept across the Fermi sea. The accepted model is valid under assumption of strong interaction equivalent to the condition of wide resonance [28].…”

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Molecular production at a broad Feshbach resonance in a Fermi gas of cooled atoms

Sun¹,

Abanov²,

Pokrovsky³

2008

Europhys. Lett.

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The problem of molecular production from degenerate gas of fermions at a wide Feshbach resonance, in a single-mode approximation, is reduced to the linear Landau-Zener problem for operators. The strong interaction leads to significant renormalization of the gap between adiabatic levels. In contrast to static problem the close vicinity of exact resonance does not play substantial role. Two main physical results of our theory is the high sensitivity of molecular production to the initial value of magnetic field and generation of a large BCS condensate distributed over a broad range of momenta in inverse process of the molecule dissociation.In recent years there have been numerous achievements in the area of ultra-cold atomic physics. The major experimental tool for it is the use of the Feshbach resonances (FR) [1,2,3,4,5,6,7], which occurs when the energy of a quasibound molecular state becomes equal to the energy of two free alkali atoms. The magneticfield dependence of the resonance allows precise tuning of the atom-atom interaction strength in an ultracold gas [1]. Moreover, time-dependent magnetic fields can be used to reversibly convert atom pairs into weakly bound molecules [8,9,10,11,12,13,14,15]. This technique has proved to be extremely effective in converting degenerate atomic gases of fermions [8,9,10,11,16,17,18] and bosons [14,15,19] into bosonic dimer molecules.The Feshbach resonance proceeds at sufficiently strong magnetic fields so that electronic spins are polarized. The collisions in s-channel of such Fermi-atoms is possible only if they have different states of nuclear spins. In a typical experiment [8,17] an admixture of atoms of 40 K with the same total atomic spin 9/2 but different spin projection quantum numbers −7/2 and −9/2 was used.Theoretical works on the molecular production can be roughly divided in two categories. The first is a phenomenology suggesting that the pairs of molecules perform independently the Landau-Zener (LZ) transitions [4,6]. Therefore the total number of molecules in the end of the process is the LZ transition probability multiplied by the number of pairs. The most problematic in this approach is what should be accepted for the LZ transition matrix element ∆ (further we call it the LZ gap). Direct calculation of the transition probability from a microscopic Hamiltonian up to the 4-th order in the interaction constant [20] shows that, in contrast to the assumption of phenomenological works, the many-body effects are very essential. Another category includes the works based on a simplified model [21], in which molecules have only one available state mimicking the condensate [22,23,24]. Though the numerical works of this category displayed a reasonable temperature dependence, they could not give a clear physical picture and detailed dependencies on parameters of the problem. The series of semi-analytical works by Pazy et al. [22,25,26,27] were based on two contradicting assumptions as we show later.In this letter we consider the process of molecule production from fermi...

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Adiabatic passage through a Feshbach resonance in a degenerate quantum gas

Cited by 4 publications

References 20 publications

Dynamics of an electric dipole moment in a stochastic electric field

Dynamics of an electric dipole moment in a stochastic electric field

Molecules with an induced dipole moment in a stochastic electric field

Molecular production at a broad Feshbach resonance in a Fermi gas of cooled atoms

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