Transparent control of three-body selective destruction of tunneling via unusual states

Abstract

We study transparent control of quantum tunneling via unusual analytical solutions for three bosons held in a driven double-well. Under high-frequency approximation, we analytically obtain the fine band structure and general non-Floquet state. At some collapse points of the quasi-energy spectra, the latter becomes the unusual special states. Based on the analytical results and their numerical correspondences, we clearly reveal the mechanism of coherent tunneling and suggest a scheme to transparently control the tunneling of three bosons from one well to another. The results can be observed with the current experimental capability (Chen et al 2011 Phys. Rev. Lett. 107 210405)

Coherent control of spin tunneling in a spin-orbit coupled bosonic triple well

“…, 0, ↓ is the Floquet state with the same period as the Hamiltonian (1). According to the superposition principle of quantum mechanics, the non-Floquet state can be constructed by the linear superposition of the Floquet states, which implies a quantum interference effect among the Floquet states with different quasienergy [25,[34][35][36]. We have introduced the stationary solution of equation ( 4) as b k (t) = A k e −iEt with A k being constant.…”

“…This will result in the quasienergies E 3 = E 5 = − α/2 and E 4 = E 6 = α/2, which means that the new quasienergy degeneracy occurs. To our knowledge, the degeneracy of energy levels generally implies quantum decoherence, so it will lead to the intriguing phenomenon of quantum tunneling, for instance, the selective coherent destruction of tunneling (SCDT) takes place at the degeneracy (crossing) point of the partial energy levels [34][35][36] and coherent destruction of tunneling (CDT) occurs at the collapse (crossing) point of all energy levels [37,38]. As an example, we set the parameters γ = 0.5, ω = 50, Ω = 100, ν = 1, and (a) ε 2 = 5.1356ω, (b) ε 2 = 2ω to plot the quasienergy spectra with quasienergy as a function of the driving parameter ε 1 /ω, as in figure 1(a)-(b), respectively.…”

Coherent control of quasi-degenerate stationary-like states via multiple resonances

“…When the SLSs have the same Floquet quasienergy, the transitions between them cannot be directly related to the observable multiphoton absorption 15 , 16 . We define such SLSs as quasi-degenerate stationary-like states (QDSLSs), including the CDT (coherent destruction of tunneling) single state with only a single Fock basis 33 , and the NOON state (a superposition of N particles in well 1 with zero particle in well 2 and vice versa) 30 . We will demonstrated that the QDSLSs may be prepared by using the multiple-resonance effects.…”

“…We will demonstrated that the QDSLSs may be prepared by using the multiple-resonance effects. Then we define SCDT (selective coherent destruction of tunneling) state as a superposition of n Fock states with time-dependent occupied probabilities, where n is less than the dimension of the considered Hilbert space 33 . In such a state, transition of the system to any one of the lacked Fock states can be suppressed selectively.…”

“…Within the high-frequency approximation and for multiple-resonance conditions, we analytically obtain all Floquet eigenstates and quasienergies. When the driving parameters and initial conditions are adjusted appropriately, a superposition state of Floquet states becomes one of the QDSLSs or a SCDT state 33 – 35 that means the transitions between some states are suppressed selectively and the Rabi oscillations between the other QDSLSs occur. Thus the coherent control of quantum transitions between QDSLSs with the same Floquet quasienergy can be realized transparently via the analytical solutions.…”