Dynamic steady-state of periodically-driven quantum systems

Abstract

Using the density matrix formalism, we prove an existence theorem of the periodic steady-state for an arbitrary periodically-driven system. This state has the same period as the modulated external influence, and it is realized as an asymptotic solution ($t$$\to$$+\infty$) due to relaxation processes. The presented derivation simultaneously contains a simple computational algorithm non-using both Floquet and Fourier theories, i.e. our method automatically guarantees a full account of all frequency components. The description is accompanied by the examples demonstrating a simplicity and high efficiency of our method. In particular, for three-level $\Lambda$-system we calculate the lineshape and field-induced shift of the dark resonance formed by the field with periodically modulated phase. For two-level atom we obtain the analytical expressions for signal of the direct frequency comb spectroscopy with rectangular light pulses. In this case it was shown the radical dependence of the spectroscopy lineshape on pulse area. Moreover, the existence of quasi-forbidden spectroscopic zones, in which the Ramsey fringes are significantly reduced, is found. The obtained results have a wide area of applications in the laser physics and spectroscopy, and they can stimulate the search of new excitation schemes for atomic clock. Also our results can be useful for many-body physics.

8 pages, 8 figures

References in corpus (21)

• Photonic Floquet Topological Insulators
• Floquet Topological Insulator in Semiconductor Quantum Wells
• Dynamical control of matter-wave tunneling in periodic potentials
• Equilibrium states of generic quantum systems subject to periodic driving
• Many-body localization in periodically driven systems
• Non-Abelian gauge fields and topological insulators in shaken optical lattices
• Periodically driven ergodic and many-body localized quantum systems
• Many-body energy localization transition in periodically driven systems
• Periodic steady state and interference in a periodically driven quantum system
• Nonlinear magneto-optical rotation with frequency-modulated light in the geophysical field range
• Nonlinear Magneto-Optical Rotation with Amplitude-Modulated Light: AMOR
• Generalized Bose-Einstein condensation into multiple states in driven-dissipative systems
• Dynamical Stability of a Many-body Kapitza Pendulum
• Isotropic magnetometry with simultaneous excitation of orientation and alignment CPT resonances
• Stability of a Floquet Bose-Einstein condensate in a one-dimensional optical lattice
• Floquet control of quantum dissipation in spin chains
• Nonlinear magneto-optical rotation with modulated light in tilted magnetic fields
• Atomic clocks with suppressed blackbody radiation shift
• A high-sensitivity push-pull magnetometer
• Linear response as a singular limit for a periodically driven closed quantum system
• Modulation induced frequency shifts in a CPT-based atomic clock

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• Towards improved loading, cooling, and trapping of molecules in magneto-optical traps
• Reservoir engineering of Cooper-pair-assisted transport with cold atoms
• Dynamic continuous-wave spectroscopy of coherent population trapping at phase-jump modulation
• Interrogating the temporal coherence of EUV frequency combs with highly charged ions
• Periodically Driven Open Quantum Systems: Spectral Properties and Non-Equilibrium Steady States
• Adaptive Rotating-Wave Approximation for Driven Open Quantum Systems
• Harmonic dual dressing of spin one-half systems
• Tunable quantum interference effects in Floquet two- and three-level systems
• Steady state of periodically driven quantum systems