PTspectroscopy of the Rabi problem

Abstract

We investigate the effects of a time-periodic, non-hermitian, PT -symmetric perturbation on a system with two (or few) levels, and obtain its phase diagram as a function of the perturbation strength and frequency. We demonstrate that when the perturbation frequency is close to one of the system resonances, even a vanishingly small perturbation leads to PT symmetry breaking. We also find a restored PT -symmetric phase at high frequencies, and at moderate perturbation strengths, we find multiple frequency windows where PT -symmetry is broken and restored. Our results imply that the PT -symmetric Rabi problem shows surprisingly rich phenomena absent in its hermitian or static counterparts. Introduction.A two-level system coupled to a sinusoidally varying potential is a prototypical example of a time-dependent, exactly solvable Hamiltonian, with profound implications to atomic, molecular, and optical physics [1]. When the frequency of perturbation ω is close to the characteristic frequency ∆ of the two-level system -near resonance -the system undergoes complete population inversion for an arbitrarily small strength γ of the potential [2]. The implications of this result to spin magnetic resonance, Rabi flopping [3], and its generalization, namely the Jaynes-Cummings model [4,5], have been extensively studied over the past half century [6,7]. Surprisingly, the quantum Rabi problem, where the full quantum nature of the perturbing bosonic field is taken into account, has only been recently solved [8].The two-level model is useful because it is applicable to many-level systems when the perturbation frequency is close to or resonant with a single pair of levels. As the detuning away from resonance |∆ − ω| increases, the perturbation strength necessary for population inversion increases linearly with it; in a many-level system, with increased potential strength, transitions to other levels have to be taken into account and the resultant problem is not exactly solvable. Therefore, understanding the behavior of a system in the entire parameter space (γ, ω) requires analytical and numerical approaches. All of these studies are restricted to hermitian potentials.In recent years, discrete Hamiltonians with a hermitian tunneling term H 0 and a non-hermitian perturbation V that are invariant under combined parity and timereversal (PT ) operations have been extensively investigated [9][10][11][12][13][14][15][16]. The spectrum λ of a PT -symmetric Hamiltonian is real when the strength γ of the non-hermitian perturbation is smaller than a threshold γ P T set by the hermitian tunneling term. Traditionally, the emergence of complex-conjugate eigenvalues that occurs when the threshold is exceeded, γ > γ P T , is called PT symmetry breaking [17][18][19]. It is now clear that PT -symmetric Hamiltonians represent open systems with balanced gain and loss, and PT symmetry breaking is a transition from a quasiequilibrium state (PT -symmetric state) to

Stabilizing non-Hermitian systems by periodic driving

“…Extended unitarity realized by periodic driving is expected to be more useful than what is learned here. We also note a recent stimulating study [35], where the emphasis is placed on how PT -symmetry of driven systems is broken by a close-to-resonance perturbation. The mapping found here can be used to explain some results in Ref.…”

Analytical results for a parity-time-symmetric two-level system under synchronous combined modulations

“…Thus, three distinct modified pulse area conditions for CPI in the non-Hermitian two-level system (1) have been identified, which are dependent on the choice of the proportional constant R and given by Eqs. (30), (33) and (36) respectively.…”

Nonlinear switching and solitons in PT‐symmetric photonic systems

“…Such a model type was found to possess PT symmetry, under certain restrictions on the modulation profiles [178][179][180]. The formulation of Eq.…”

“…PT diagram for harmonic modulation, γ 1 = −γ 2 ∼ cos(ωz) was calculated in Ref. [179], see Fig. 28(b).…”

“…Modulation of structure parameters along the propagation direction of coupled optical waveguides with gain and loss can open new opportunities for optical signal control in both linear [178][179][180] and nonlinear [67,82,[181][182][183][184][185] regimes.…”