Nonlinear Adiabatic Passage from Fermion Atoms to Boson Molecules

Mean-field approach has recently been used to model coupled atom-molecular Bose-Einstein condensates (BEC) and coupled Fermi-Bose condensates near Feshbach resonance. Sweeping of magnetic field across the resonance gives a new (nonlinear) version of Landau-Zener problem. We investigate the structure of the corresponding classical phase space and calculate change in the action which corresponds to finite-rate efficiency of the sweep. We consider the case of non-zero initial action, which corresponds to some finite initial molecular fraction. * Electronic address: alx˙it@yahoo.com 2

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“…The system can also be investigated using the equations of motion for a generalized Bloch vector [14]:u…”

Section: Main Equations and Phase Portraitsmentioning

confidence: 99%

“…For example, in [14], the model (1) with zero fermionic bandwidth and time-dependent molecular energy was considered using another approach (similar to that of [17]). To be more precise, [14] considers the Hamiltonian H = k,σ ǫ k c the association of a quantum-degenerate gas of fermions,…”

Section: Introductionmentioning

confidence: 99%

Change in the adiabatic invariant in a nonlinear two-mode model of Feshbach resonance passage

Itin

Vasiliev

Krishna

et al. 2007

Physica D: Nonlinear Phenomena

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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].…”

mentioning

confidence: 80%

“…This assumption was justified for the equilibrium state in the case of wide resonance [28] and used in the most of theoretical works on the dynamics of transition [5,25,26,27,29]. We thus replaceb q in Eq.…”

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confidence: 99%

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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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Applications of Nonlinear Adiabatic Evolution

Liu

et al. 2018

Nonlinear Adiabatic Evolution of Quantum Systems

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Nonlinear Adiabatic Passage from Fermion Atoms to Boson Molecules

Cited by 36 publications

References 25 publications

Change in the adiabatic invariant in a nonlinear two-mode model of Feshbach resonance passage

Change in the adiabatic invariant in a nonlinear two-mode model of Feshbach resonance passage

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

Applications of Nonlinear Adiabatic Evolution

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