Weak coupling regime of the Landau-Zener transition for association of an atomic Bose-Einstein condensate

Sahakyan, N.; Azizbekyan, H.; Ishkhanyan, H. A.; Sokhoyan, Ruzan; Ishkhanyan, А. М.

doi:10.1134/s1054660x10010184

Cited by 10 publications

(4 citation statements)

References 16 publications

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“…PA bounds together atoms of two different alkali species into excited state molecules that can decay by spontaneous emission into (meta-) stable molecules. The process produces molecules that are generally distributed in high-lying rovibrational levels of the ground singlet or lowest metastable triplet state [9,10], while evidence for the spontaneous creation of deeply-bound ground state polar bi-alkali molecules such as KRb [11], LiCs [12], and NaCs [13,14] has been reported. Molecules in high-lying vibrational levels have a weakly polar character but represents a starting point for a further manipulation that can transfer them into the lowest vibrational level v=0.…”

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confidence: 99%

Formation of ultracold RbCs molecules by photoassociation

et al. 2012

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The formation of ultracold metastable RbCs molecules is observed in a double species magneto-optical trap through photoassociation below the ^85Rb(5S_1/2)+^133Cs(6P_3/2) dissociation limit followed by spontaneous emission. The molecules are detected by resonance enhanced two-photon ionization. Using accurate quantum chemistry calculations of the potential energy curves and transition dipole moment, we interpret the observed photoassociation process as occurring at short internuclear distance, in contrast with most previous cold atom photoassociation studies. The vibrational levels excited by photoassociation belong to the 5th 0^+ or the 4th 0^- electronic states correlated to the Rb(5P_1/2,3/2)+Cs(6S_1/2) dissociation limit. The computed vibrational distribution of the produced molecules shows that they are stabilized in deeply bound vibrational states of the lowest triplet state. We also predict that a noticeable fraction of molecules is produced in the lowest level of the electronic ground state

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confidence: 99%

Formation of ultracold RbCs molecules by photoassociation

et al. 2012

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“…Here, ) , ( 1 t p LZ λ is the solution of the linear Landau-Zener problem for an effective 1 λ [26]:…”

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confidence: 99%

Variational ansatz for the nonlinear Landau–Zener problem for cold atom association

Ishkhanyan

Joulakian²,

Suominen

2009

J. Phys. B: At. Mol. Opt. Phys.

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We present a rigorous analysis of the Landau-Zener linear-in-time term crossing problem for quadratic-nonlinear systems relevant to the coherent association of ultracold atoms in degenerate quantum gases. Our treatment is based on an exact third-order nonlinear differential equation for the molecular state probability. Applying a variational two-term ansatz, we construct a simple approximation that accurately describes the whole-time dynamics of coupled atom-molecular system for any set of involved parameters. Ensuring an absolute error less than 5 10 − for the final transition probability, the resultant solution improves by several orders of magnitude the accuracy of the previous approximations by A. Ishkhanyan et al. developed separately for the weak coupling [J. Phys. A 38, 3505 (2005)] and strong interaction [J. Phys. A 39, 14887 (2006)] limits. In addition, the constructed approximation covers the whole moderate-coupling regime, providing for this intermediate regime the same accuracy as for the two mentioned limits. The obtained results reveal the remarkable observation that for the strong-coupling limit the resonance crossing is mostly governed by the nonlinearity, while the coherent atom-molecular oscillations arising soon after the resonance has been crossed are basically of linear nature. This observation is supposed to be of a general character due to the basic attributes of the resonance crossing processes in the nonlinear quantum systems of the discussed type of involved quadratic nonlinearity.

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“…Over last decades, growing attention has also been paid to non-Hermitian extensions of the classic theory, taking into account the effect of environment on two-level systems (e.g., [13][14][15] and references therein). Due to its generality, the Landau-Zener scenario has been applied to numerous problems in various contexts, such as laser physics [16], semiconductor superlattices [17], tunneling of optical [18] or acoustic [19,20] waves, and quantum information processing [21], to name just a few examples. Although a passage between two energy levels is an intrinsic feature of all above-mentioned processes, the demonstration of a direct connection between energy transfer in a classical oscillatory system with time-dependent parameters and nonadiabatic quantum Landau-Zener tunneling is a recent development.…”

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confidence: 99%

Fresnel integrals and irreversible energy transfer in an oscillatory system with time-dependent parameters

2011

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We demonstrate that in significant limiting cases the problem of irreversible energy transfer in an oscillatory system with time-dependent parameters can be efficiently solved in terms of the Fresnel integrals. For definiteness, we consider a system of two weakly coupled linear oscillators in which the first oscillator with constant parameters is excited by an initial impulse, whereas the coupled oscillator with a slowly varying frequency is initially at rest but then acts as an energy trap. We show that the evolution equations of the slow passage through resonance are identical to the equations of the Landau-Zener tunneling problem, and therefore, the suggested asymptotic solution of the classical problem provides a simple analytic description of the quantum Landau-Zener tunneling with arbitrary initial conditions over a finite time interval. A correctness of approximations is confirmed by numerical simulations.

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Weak coupling regime of the Landau-Zener transition for association of an atomic Bose-Einstein condensate

Cited by 10 publications

References 16 publications

Formation of ultracold RbCs molecules by photoassociation

Formation of ultracold RbCs molecules by photoassociation

Variational ansatz for the nonlinear Landau–Zener problem for cold atom association

Fresnel integrals and irreversible energy transfer in an oscillatory system with time-dependent parameters

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