Demkov-kunike model for cold atom association: Weak interaction regime

Sokhoyan, Ruzan; Azizbekyan, H.; Leroy, Claude; Ishkhanyan, А. М.

doi:10.3103/s1068337209060036

Cited by 7 publications

(12 citation statements)

References 23 publications

(37 reference statements)

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“…The first DK model denoted as DK1 is characterized by a bellshaped pulse (see figure 1) and a time-dependent interaction (Rabi frequency) of hyperbolic-secant shape while in the second DK model (DK2), the Rabi frequency is constant in time 7,19 . Both models are convenient for finiteduration pulses and have proven to be applicable in: the physics of ultracold trapped gases 22 , superchemistry 23 , Bose-Einstein condensates 24 , photo-and magneto-asso-ciation for production of cold molecules 25 .…”

Section: Introductionmentioning

confidence: 99%

Demkov-Kunike models with decay

Kenmoe

Tchapda

Fai

2016

Journal of Mathematical Physics

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Exact analytical solutions to the dissipative time-dependent Schrödinger equation are obtained for a decaying two-state system with decay rates Γ 1 and Γ 2 for levels with extremal spin projections. The system is coherently driven with a pulse whose detuning is made up of two parts: a time-dependent part (chirp) of hyperbolictangent shape and a static part with real and imaginary terms. This gives us a wide range of possibilities to arbitrarily select the interaction terms. We considered two versions which led to decaying Demkov-Kunike (DK) models; the version in which the Rabi frequency (interaction) is a time-dependent hyperbolic-secant function (called decaying DK1 model) and the case when it is constant in time and never turns off (decaying DK2 model). Our analytical solutions account for all possible initial moments instead of only t 0 = 0 or t 0 = −∞ as for non-decaying models and may be useful for experiments on level crossings. Two complementary limits of the pulse detuning are considered and explored: the limit of fast (i) and slow rise (ii). In the case (i), the coupling between level positions in the first DK model collapses while the second DK model reduces to a Rabi model (constant Hamiltonian), in the case (ii), both DK models reduce to the LZ model. In both cases (i) and (ii), analytical approximated solutions which conveniently approach the exact solutions are derived.

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Section: Introductionmentioning

confidence: 99%

Demkov-Kunike models with decay

Kenmoe

Tchapda

Fai

2016

Journal of Mathematical Physics

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“…[8][9][10][11][12][13][14][15][16][17][18][19][20]) have mostly been focused on the treatment of the Landau-Zener (LZ) model [21]. In the case of photoassociation the LZ model describes a situation when the two quantum states are coupled by an external optical field of constant amplitude and a variable frequency, which is linearly changed in time.…”

Section: Introductionmentioning

confidence: 99%

“…[23], where an analytical formula describing the temporal dynamics of the molecule formation has been obtained. The strong interaction limit of the DK model, corresponding to large values of the peak laser field amplitude, has been studied in Refs.…”

Section: Introductionmentioning

confidence: 99%

“…The weak interaction limit of the nonlinear DK problem, corresponding to small values of the peak laser field amplitude, has recently been discussed in Ref. [23], where an analytical formula describing the temporal dynamics of the molecule formation has been obtained. The strong interaction limit of the DK model, corresponding to large values of the peak laser field amplitude, has been studied in Refs.…”

Section: Introductionmentioning

confidence: 99%

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An ansatz for the nonlinear Demkov-Kunike problem for cold molecule formation

Azizbekyan

2010

J. Contemp. Phys.

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Abstract. We study nonlinear mean-field dynamics of ultracold molecule formation in the case when the external field configuration is defined by the level-crossing Demkov-Kunike model, characterized by a bellshaped coupling and finite variation of the detuning. Analyzing the fast sweep rate regime of the strong interaction limit, which models a situation when the peak value of the coupling is large enough and the resonance crossing is sufficiently fast, we construct a highly accurate ansatz to describe the temporal dynamics of the molecule formation in the mentioned interaction regime. The absolute error of the constructed approximation is less than for the final transition probability while at certain time points it might increase up to . Examining the role of the different terms in the constructed approximation, we prove that in the fast sweep rate regime of the strong interaction limit the temporal dynamics of the atom-molecule conversion effectively consists of the process of resonance crossing, which is governed by a nonlinear equation, followed by atom-molecular coherent oscillations which are basically described by a solution of the linear problem, associated with the considered nonlinear one. IntroductionAfter the realization of Bose-Einstein condensation (BEC) [1] in dilute gases of neutral alkalimetal atoms, the next challenge was to achieve a BEC of molecules. Molecules have complex internal structure and, therefore, more degrees of freedom, thus they offer a vast range of properties not available in the case of atoms. However, in contrast to atomic condensates, achieving molecular condensates via standard laser cooling techniques [2] is practically impossible, because of the rovibrational spectrum of the molecules. Consequently, the Raman photoassociation [3] and magnetic Feshbach resonance [4] have become the standard tools to create cold molecules starting from ultracold atomic gases [5][6][7].So far, the theoretical efforts to describe the dynamics of cold molecule formation (e.g., see Refs. [8][9][10][11][12][13][14][15][16][17][18][19][20]) have mostly been focused on the treatment of the Landau-Zener (LZ) model [21]. In the case of photoassociation the LZ model describes a situation when the two quantum states are coupled by an external optical field of constant amplitude and a variable frequency, which is linearly changed in time. But this situation has some drawbacks; it is unrealistic to have a constant coupling that never turns off or infinite energies at . However, there exists a model that has all the virtues of the LZ model and is free from its shortcomings. Such a model is the first Demkov-Kunike (DK) quasilinear level-crossing model of a bell-shaped pulse (vanishing at

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“…The weak interaction limit, corresponding to small values of the Rabi frequency, has been discussed in 26,27 . Applying Picard's successive approximations to an exact nonlinear Volterra integral equation 26 or a specific variational approach involving the solution of the associated linear problem 27 , analytical approximations for the probability of transition to the molecular state at +∞ → t have been obtained. The strong coupling limit, corresponding to large values of Rabi frequency, has been addressed in 21,22,28,29 .…”

Section: Introductionmentioning

confidence: 99%

Demkov-Kunike model in cold molecule formation

Ishkhanyan

2010

SPIE Proceedings

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We study the dynamics of cold molecule formation via photo- or magneto-association of quantum degenerate atomic gases for the case when the field configuration is defined by the quasi-linear level crossing Demkov-Kunike model, which is characterized by a bell-shaped pulse and finite variation of the frequency detuning. We generalize the approach developed for the Landau-Zener model and propose a cubic polynomial equation for the asymptotic transition probability at infinity applicable in the large detuning regime of the interaction process. The proposed approximation applies to all values of the Rabi frequency; hence, it presents a unified description of previously noticed weak, moderate, and strong interaction limits of the fast sweep regime. This cubic equation for the transition probability provides improvement of previous results by an order of the magnitude

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Demkov-kunike model for cold atom association: Weak interaction regime

Cited by 7 publications

References 23 publications

Demkov-Kunike models with decay

Demkov-Kunike models with decay

An ansatz for the nonlinear Demkov-Kunike problem for cold molecule formation

Demkov-Kunike model in cold molecule formation

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