Dynamical control in a quasi-periodically modulated optical lattice

Abstract

-We investigate quantum tunneling phenomena for an optical lattice subjected to a bichromatic ac force. We show that incommensurability of the frequencies leads to super Bloch oscillation. We propose directed super Bloch oscillation for the quasi periodically driven optical lattice. We study the dynamical localization and photon assisted tunneling for a periodical and quasi-periodical ac force.Introduction. -Quantum tunneling of particles between potential wells is a fundamental concepts in physics and used to perform measurements of forces with high sensitivity and accuracy [1]. Recent experiments on cold atoms in optical lattices subject to time-periodic perturbations have revealed details of tunneling control through an external driving field. Tunneling control in optical lattices depends in general on the form of the external potential and, in particular, on its parameters. Nontrivial dynamical effects have been demonstrated even in the absence of nonlinear atom-atom interaction. In an optical lattice, the Bloch states are completely delocalized, with the atomic wave functions extending over the whole lattice. Thus, an initially localized wave-packet spreads ballistically in time. The presence of dc force breaks the translational symmetry and suppress atomic tunneling [2,3]. The physical picture changes if the external force is ac type (optical lattice are periodically shaken back and forth). The effect of an ac force is the reduced tunneling rate. At certain shaking strengths, tunneling is lost and dynamical localization occurs [4,5]. The combined presence of both dc and ac forces leads interesting results such as directed motion, super Bloch oscillation and photon-assisted tunneling. Super Bloch oscillations over hundreds of lattice sites occur when an integer multiple of the ac frequency is slightly detuned from the Bloch frequency associated with the dc component of the force [6][7][8][9][10][11][12]. In photon assisted tunneling, wavepacket delocalization occurs for an initially localized wave packet when modulation frequency is at multiple integers of the Bloch frequency [13][14][15][16][17][18][19]. It was shown that not only the strength of the ac force but also its phase is of experimental relevance [20,21]. The generalization of the monochromatic ac force to a multi-frequency ac force leads to nontrivial results in ultra cold atom dynamics [22][23][24][25][26][27][28][29][30][31][32][33]. The relationship between symmetries and transport was explored for a cold atom ratchet with multifrequency driving [25]. It was shown that the bi-harmonic ac force stabilizes the dynamics, allowing the generation of uniform directed motion over a range of momentum much larger than what is possible with a dc bias [29]. In this paper, we study quantum tunneling phenomena for an optical lattice subjected to a

Quasi-Periodically Driven Quantum Systems

“…In the regime where the fluctuations can be neglected, however, their regularity is irrelevant. This supports the view that, as quasi-periodic functions provide a more general parameterisation of the driving protocol, quasi-periodically driven quantum systems have the potential to expand the accessible effective dynamics in a variety of experimental setups [67].…”

Controlling migration of a pair of correlated particles by doubly modulated fields

“…, which will recover the resonant tunneling case. A quasi-periodic driving lattice also reveal the possibility of vanishing hopping rates [40]. In our situation, when K U w w takes an irrational number, e.g., 2…”

Super Bloch oscillation in aPTsymmetric system

“…One can use high-frequency Floquet approach to construct a time-independent effective Hamiltonian to study the spectrum of the periodical Hamiltonian. In this approach, which is valid if ω 0 is large, the tunneling parameter is replaced by an effective tunneling parameter, T e f f. [9,29,30]…”

“…However, tunneling is partially restored if an additional oscillating force is also present in the system. This effect is known as photon assisted tunneling [9] since the role of the photons is played by the oscillation of the force at resonant frequencies. In our system, partial restoration of the tunneling increases γ PT .…”

“…In this case, wave packet delocalization occurs for an initially localized wave packet when modulation frequency is at multiple integers of the Bloch frequency [6]. Another interesting effect is the super Bloch oscillations, which arises when an integer multiple of the oscillation frequency is only slightly detuned from the Bloch frequency associated with the constant force [7,8,9,10,11,12]. Note that the amplitude of super Bloch oscillation is much larger than that of Bloch oscillation.…”