Landau-Zener transitions and adiabatic impulse approximation in an array of two Rydberg atoms with time-dependent detuning

Niranjan, Ankita; Li, Weibin; Nath, Rejish

doi:10.1103/physreva.101.063415

Cited by 26 publications

(24 citation statements)

References 107 publications

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“…In this subsection, we investigate the relationship between AIA, an approximation method that has been used so far, and GAIA proposed here. There are two types of AIAs: those using energy basis | i (t) [17,23] and those using diabatic basis |i [22,24]. Both approximation methods use instantaneous eigenvalues to describe the adiabatic time evolution, which has a disadvantage of being difficult to compute analytically for multilevel systems.…”

Section: Comparison With Aiamentioning

confidence: 99%

“…Its Hamiltonian has diagonal elements that depend linearly on time, while off-diagonal elements are time-independent [7][8][9][10]. The dynamics of such nonadiabatic transitions has attracted much attention in various fields and physical systems: quantum information science [11,12], chemical physics [13], atomic physics [14][15][16][17], circuit-QED system [18,19], ultracold atom system [20], and quantum dot system [21]. In general, however, solving the Schrödinger equation for the timedependent multilevel system is difficult.…”

Section: Introductionmentioning

confidence: 99%

“…This is an approximation under which the system evolves adiabatically except when the energy gap becomes small and non-adiabatic transition occurs instantaneously. Since it requires information on instantaneous eigenvalues, this approximation can only be used for relatively small systems such as two-and three-level systems [17,24].…”

Section: Introductionmentioning

confidence: 99%

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Generalized Adiabatic Impulse Approximation

Suzuki,

Nakazato

2021

Preprint

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Non-adiabatic transitions in multilevel systems appear in various fields of physics, but it is not easy to analyze their dynamics in general. In this paper, we propose to extend the adiabatic impulse approximation to multilevel systems. This approximation method is shown to be equivalent to a series of unitary evolutions and facilitates to evaluate the dynamics numerically. In particular, we analyze the dynamics of the Landau-Zener grid model and the multilevel Landau-Zener-Stückelberg-Majorana interference model, and confirm that the results are in good agreement with the exact dynamics evaluated numerically. We also derive the conditions for destructive interference to occur in the multilevel system. II. REVIEW : EXACT WKB ANALYSIS FOR THREE-LEVEL LZ MODELIn this section, we present a brief review of the exact-WKB analysis for the three-level LZ model in previous studies [53,54]. Consider the following Schrödinger equa-

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Section: Comparison With Aiamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Generalized Adiabatic Impulse Approximation

Suzuki,

Nakazato

2021

Preprint

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“…The Rydberg blockade, in which strong Rydberg-Rydberg interactions (RRIs) suppress simultaneous excitation of two Rydberg atoms within a finite volume [36][37][38][39], and the breaking of the blockade (anti-blockade) [40][41][42][43] are of central utility for these applications. For two atoms, it has been predicted that through modulation induced resonances, one can engineer the parameter space for both Rydberg-blockade and anti-blockade [44][45][46]. The latter is proposed to have applications in implementing robust quantum gates [46][47][48] and accelerating the formation of dissipative entangled steady states [49].…”

Section: Introductionmentioning

confidence: 99%

Population trapping in a pair of periodically driven Rydberg atoms

Mallavarapu

Niranjan

et al. 2021

Phys. Rev. A

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We study the population trapping extensively in a periodically driven Rydberg pair. The periodic modulation of the atom-light detuning effectively suppresses the Rabi couplings and, together with Rydberg-Rydberg interactions, leads to the state-dependent population trapping. We identify a simple yet a general scheme to determine population trapping regions using driving induced resonances, the Floquet spectrum, and the inverse participation ratio. Contrary to the single atom case, we show that the population trapping in the two-atom setup may not necessarily be associated with level crossings in the Floquet spectrum. Further, we discuss under what criteria population trapping can be related to dynamical stabilization, taking specific and experimentally relevant initial states, which include both product and the maximally entangled Bell states. The behavior of the entangled states is further characterized by the bipartite entanglement entropy.

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“…As this energy separation changes sign, the diabatic states (i.e., eigenstates of the Hamiltonian in the absence of tunneling) undergo a level crossing, while the adiabatic states (i.e., eigenstates of the Hamiltonian in the presence of tunneling) encounter an avoided crossing. Characterizing both the nonadiabatic and the adiabatic transitions, the LZ model has been widely adopted to describe and understand fundamental physical problems in various fields, including atomic and molecular physics [7][8][9][10][11][12], chemical physics [13], and quantum information science [14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Photon-assisted Landau-Zener transitions in a periodically driven Rabi dimer coupled to a dissipative mode

Zheng,

Shen,

Sun

et al. 2021

Preprint

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We investigate multiple photon-assisted Landau-Zener (LZ) transitions in a hybrid circuit quantum electrodynamics device in which each of two interacting transmission-line resonators is coupled to a qubit, and the qubits are driven by periodic driving fields and also coupled to a common phonon mode. The quantum state of the entire composite system is modeled using the multi-D2 Ansatz in combination with the time-dependent Dirac-Frenkel variational principle. Applying a sinusoidal driving field to one of the qubits, this device is an ideal platform to study the photon-assisted LZ transitions by comparing the dynamics of the two qubits. A series of interfering photon-assisted LZ transitions take place if the photon frequency is much smaller than the driving amplitude. Once the two energy scales are comparable, independent LZ transitions arise and a transition pathway is revealed using an energy diagram. It is found that both adiabatic and nonadiabatic transitions are involved in the dynamics. Used to model environmental effects on the LZ transitions, the common phonon mode coupled to the qubits allows for more available states to facilitate the LZ transitions. An analytical formula is obtained to estimate the short-time phonon population and produces results in reasonable agreement with numerical calculations. Equipped with the knowledge of the photonassisted LZ transitions in the system, we can precisely manipulate the qubit state and successfully generate the qubit dynamics with a square-wave pattern by applying driving fields to both qubits, opening up new venues to manipulate the states of qubits and photons in quantum information devices and quantum computers.

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Landau-Zener transitions and adiabatic impulse approximation in an array of two Rydberg atoms with time-dependent detuning

Cited by 26 publications

References 107 publications

Generalized Adiabatic Impulse Approximation

Generalized Adiabatic Impulse Approximation

Population trapping in a pair of periodically driven Rydberg atoms

Photon-assisted Landau-Zener transitions in a periodically driven Rabi dimer coupled to a dissipative mode

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