An analytical double-unitary-transformation approach for strongly and periodically driven three-level systems

• URL: http://arxiv.org/abs/2001.10733v1
• Date: Wed, 29 Jan 2020 09:07:49 GMT
• Title: An analytical double-unitary-transformation approach for strongly and periodically driven three-level systems
• Authors: Yingying Han, Xiao-Qing Luo, Tie-Fu Li, and Wenxian Zhang
• Abstract summary: We develop a double-unitary-transformation approach to deal with periodically modulated and strongly driven systems. We harness the generalized Van Vleck perturbation theory to deal with the transformed Floquet matrix. This method offers a useful tool to analytically study the multi-level systems with strong transverse couplings.
• Score: 2.3224139967919974
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Floquet theory combined with the generalized Van Vleck nearly degenerate perturbation theory, has been widely employed for studying various two-level systems that are driven by external fields via the time-dependent longitudinal (i.e., diagonal) couplings. However, three-level systems strongly driven by the time-dependent transverse (i.e., off-diagonal) couplings have rarely been investigated, due to the breakdown of the traditional rotating wave approximation. Meanwhile, the conventional perturbation theory is not directly applicable, since a small parameter for the perturbed part is no longer apparent. Here we develop a double-unitary-transformation approach to deal with the periodically modulated and strongly driven systems, where the time-dependent Hamiltonian has large off-diagonal elements. The first unitary transformation converts the strong off-diagonal elements to the diagonal ones, and the second enables us to harness the generalized Van Vleck perturbation theory to deal with the transformed Floquet matrix and also allows us to reduce the infinite-dimensional Floquet Hamiltonian to a finite effective one. For a strongly modulated three-level system, with the combination of the Floquet theory and the transformed generalized Van Vleck perturbation theory, we obtain analytical results of the system, which agree well with exact numerical solutions. This method offers a useful tool to analytically study the multi-level systems with strong transverse couplings.

Related papers

• The transfer of nonlocality between two- and three-qubit dissipative systems with counter-rotating-wave terms [0.13124513975412253]
  In the strong coupling regime, the counter-rotating terms accelerate the decay of genuine three-party correlations. In the ultrastrong coupling regime, we observe a novel phenomenon where nonlocality is consistently transferred between a three-qubit and its subsystem.
  arXiv  Detail & Related papers  (2024-11-21T07:34:48Z)
• Study of quantum phase transition and entanglement in coupled top systems with standard and nonstandard symmetries under Floquet formalism [15.699822139827916]
  We study an effective time-independent Hamiltonian of a coupled kicked-top (CKT) system derived using the Van Vleck-based perturbation theory at the high-frequency driving limit under Floquet formalism. We study classical and quantum versions of this coupled top system for torsion-free and nonzero torsion cases.
  arXiv  Detail & Related papers  (2024-09-13T06:36:41Z)
• Third quantization of open quantum systems: new dissipative symmetries and connections to phase-space and Keldysh field theory formulations [77.34726150561087]
  We reformulate the technique of third quantization in a way that explicitly connects all three methods. We first show that our formulation reveals a fundamental dissipative symmetry present in all quadratic bosonic or fermionic Lindbladians. For bosons, we then show that the Wigner function and the characteristic function can be thought of as ''wavefunctions'' of the density matrix.
  arXiv  Detail & Related papers  (2023-02-27T18:56:40Z)
• Structural aspects of FRG in quantum tunnelling computations [68.8204255655161]
  We probe both the unidimensional quartic harmonic oscillator and the double well potential. Two partial differential equations for the potential V_k(varphi) and the wave function renormalization Z_k(varphi) are studied.
  arXiv  Detail & Related papers  (2022-06-14T15:23:25Z)
• Non-Gaussian superradiant transition via three-body ultrastrong coupling [62.997667081978825]
  We introduce a class of quantum optical Hamiltonian characterized by three-body couplings. We propose a circuit-QED scheme based on state-of-the-art technology that implements the considered model.
  arXiv  Detail & Related papers  (2022-04-07T15:39:21Z)
• Random-Matrix Approach to Transition-State Theory [0.0]
  We calculate the average probability for transition from scattering channel coupled to the first Hamiltonian to a scattering channel coupled to the second Hamiltonian. For tunneling through a very thick barrier independence of formation and decay of the tunneling process hold more generally.
  arXiv  Detail & Related papers  (2022-02-10T09:13:54Z)
• Rotating Majorana Zero Modes in a disk geometry [75.34254292381189]
  We study the manipulation of Majorana zero modes in a thin disk made from a $p$-wave superconductor. We analyze the second-order topological corner modes that arise when an in-plane magnetic field is applied. We show that oscillations persist even in the adiabatic phase because of a frequency independent coupling between zero modes and excited states.
  arXiv  Detail & Related papers  (2021-09-08T11:18:50Z)
• Chaos and subdiffusion in the infinite-range coupled quantum kicked rotors [0.0]
  We map the infinite-range coupled quantum kicked rotors over an infinite-range coupled interacting bosonic model. In the thermodynamic limit the system is described by a set of coupled Gross-Pitaevskij equations equivalent to an effective nonlinear single-rotor Hamiltonian.
  arXiv  Detail & Related papers  (2021-02-15T22:29:01Z)
• Dissipative flow equations [62.997667081978825]
  We generalize the theory of flow equations to open quantum systems focusing on Lindblad master equations. We first test our dissipative flow equations on a generic matrix and on a physical problem with a driven-dissipative single fermionic mode.
  arXiv  Detail & Related papers  (2020-07-23T14:47:17Z)
• Markovian dynamics under weak periodic coupling [0.0]
  We derive a corresponding Markovian Master Equation under usual assumption of weak coupling. Special attention is granted to the case of uniformly (globally) modulated interaction, where some general results concerning the Floquet normal form of a solution and its stability are also addressed.
  arXiv  Detail & Related papers  (2020-04-15T11:54:26Z)
• Operator-algebraic renormalization and wavelets [62.997667081978825]
  We construct the continuum free field as the scaling limit of Hamiltonian lattice systems using wavelet theory. A renormalization group step is determined by the scaling equation identifying lattice observables with the continuum field smeared by compactly supported wavelets.
  arXiv  Detail & Related papers  (2020-02-04T18:04:51Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.