Dynamic steady-state of periodically-driven quantum systems

TL;DR

This paper proves the existence of a periodic steady-state in periodically-driven quantum systems using a density matrix approach, offering a simple computational method applicable to various quantum systems and phenomena.

Contribution

The authors introduce a novel, Floquet-free computational algorithm for analyzing the steady-state of periodically-driven quantum systems, applicable to complex atomic and many-body systems.

Findings

Derived analytical expressions for dark resonance lineshape and shift in a three-level system.

Obtained frequency comb spectroscopy signals for two-level atoms with rectangular pulses.

Discovered quasi-forbidden zones where Ramsey fringes are suppressed.

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.