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arXiv:1507.00628 · Physical Review A

Pulse design without the rotating-wave approximation

Sara Ibañez, Yichao Li, Xi Chen, Juan Gonzalo Muga

Published Dec 30, 2015• 39 citations
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Abstract

We design realizable time-dependent semiclassical pulses to invert the population of a two-level system faster than adiabatically when the rotating-wave approximation cannot be applied. Different approaches, based on the counterdiabatic method or on invariants, may lead to singularities in the pulse functions. Ways to avoid or cancel the singularities are put forward when the pulse spans few oscillations. For many oscillations an alternative numerical minimization method is proposed and demonstrated.

DOI
10.1103/physreva.92.062136

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We design realizable time-dependent semiclassical pulses to invert the population of a two-level system faster than adiabatically when the rotating-wave approximation cannot be applied. Different approaches, based on the counterdiabatic method or on invariants, may lead to singularities in the pulse functions. Ways to avoid or cancel the singularities are put forward when the pulse spans few oscillations. For many oscillations an alternative numerical minimization method is proposed and demonstrated.
Abstract In this paper, a scheme is put forward to design pulses which drive a three‐level system based on the reverse engineering with Lewis‐Riesenfeld invariant theory. The scheme can be applied to a three‐level system even when the rotating‐wave approximation (RWA) can not be used. The amplitudes of pulses and the maximal values of detunings in the system could be easily controlled by adjusting control parameters. We analyze the dynamics of the system by an invariant operator, so additional couplings are unnecessary. Moreover, the approaches to avoid singularity of pulses are studied and several useful results are obtained. We hope the scheme could contribute to fast quantum information processing without RWA.
An iterative predictor-corrector finite-difference time-domain method is used to solve the semiclassical Maxwell-Bloch system numerically without invoking any of the standard approximations such as the rotating-wave approximation. This approach permits a more exact study of self-induced transparency effects in a two-level atom. In addition to recovering the standard results, for instance, for \ensuremath{\pi}, 2\ensuremath{\pi}, and 4\ensuremath{\pi} pulses, several features in the results appear at the zeros of the driving pulse, where its time derivatives are maximum. Several ultrafast-pulse examples demonstrate that time-derivative-driven nonlinearities have a significant impact on the time evolution of a two-level atom system. Moreover, typical small-signal gain results are also obtained with our Maxwell-Bloch simulator. We illustrate that these time-derivative effects can be used to design an ultrafast, single-cycle pump pulse that completely inverts the two-level atom population. A pump-probe signal set is then used to illustrate gain in the probe signal.
Population transfer via chirped rapid adiabatic passage is studied using open quantum and semiclassical models, with and without the rotating-wave approximation. A time-dependent variational approach based on the multiple-Davydov D2_22​ trial state is employed to simulate the quantum models with an arbitrary finite mean photon number. We examine the accuracy of both the semiclassical field description and the rotating-wave approximation. Robust population transfer is identified over a wide parameter regime controlled by the laser spectral chirp and is found to be insensitive to the spin--phonon coupling strength, Gaussian pulse area, and energy gap of the two-level system.
Frequency swept pulses are used to invert population over a broad band of transition frequencies without the need for a precise calibration of the pulse amplitude. As long as the adiabatic approximation is valid, population is adiabatically inverted at each individual transition frequency of the swept range. Even though this picture fails to be true when the adiabatic approximation breaks down, population inversion can still be achieved for an appreciable range of transition frequencies and field amplitudes. We discuss population inversion in an ensemble of two-level systems by a frequency-swept pulse, the so-called constant adiabaticity pulse, without invoking the adiabatic approximation. The equations of motion are integrated by a seminumerical method to analyze population inversion in the regime where usually the adiabatic approximation is applied. The effects of resonance offset and variable pulse amplitude are described by an average Hamiltonian expansion to discuss pulse performance beyond the validity of the adiabatic approximation. As a function of the adiabaticity parameter (reciprocal of the pulse area), the inversion bandwidth increases in a stepwise fashion due to the consecutive cancellation of average Hamiltonians. The first inversion over a finite range of transition frequencies and pulse amplitudes is shown to occur for an adiabaticity parameter of 1/15.
We propose a technique for coherent population inversion of a two-state system, which uses an amplitude-modulated pulse. In the modulation-free adiabatic basis, the modulation introduces oscillating interaction between the adiabatic states. In a second rotating-wave approximation picture, this oscillating interaction induces a pair of level crossings between the energies of the adiabatic states if the modulation frequency is chosen appropriately. By suitably offsetting the modulation with respect to the center of the pulse, one can make the modulation act only in the vicinity of one of these crossings. In a higher-order adiabatic basis, this crossing shows up as an avoided crossing between the energies of the higher-order adiabatic states. As a result robust and efficient population transfer can be achieved between the adiabatic states, and hence, between the original bare states. We derive analytically the conditions on the interaction parameters for this technique and verify them with numerical simulations. Possible experimental implementations are discussed.
Here we use perturbation techniques based on the averaging method to investigate Rabi oscillations in cw and pulse-driven two-level systems (TLS's). By going beyond the rotating-wave approximation, especifically to second-order in perturbation, we obtain the Bloch-Siegert shift of the TLS resonant frequency, in which the resonant frequency increases with the driving field amplitude. This frequency shift implies that short resonant πππ-pulses in which the Rabi frequency is approximately 40\% or higher of the transition frequency do not achieve complete inversion in TLS's. Hence, guided by analytical results based on the averaging technique, we propose two methods for obtaining population inversions in the TLS driven by short πππ-pulses: one with chirping and the other with pulse shaping and near resonance blue-shifted detuning. Both methods minimize dephasing due to the Bloch-Siegert shift, reduce the dependance of the excitation of the TLS on the pulse phase, and are very effective in achieving complete population inversions.