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Physical Review A

Control of the Lamb shift by a driving field

Shuai Yang, Hang Zheng, R. Hong, Shi-Yao Zhu, Muhammad Suhail Zubairy

Published May 3, 2010• 6 citations
Publisher

Abstract

A unitary transformation approach is used to study the energy level shift of the atom coupled to both a vacuum electromagnetic field and a driving laser. The Lamb shift of the energy levels is shown to depend on the Rabi frequency and the detuning of the driving laser, which couples another pair of levels.
DOI
10.1103/physreva.81.052501

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•Dec 12, 2013•0 citations
We discuss radiative corrections to an atomic two-level system subject to an intense driving laser field. It is shown that the Lamb shift of the laser-dressed states, which are the natural state basis of the combined atom-laser system, cannot be explained in terms of the Lamb shift received by the atomic bare states which is usually observed in spectroscopic experiments. In the final part, we propose an experimental scheme to measure these corrections based on the incoherent resonance fluorescence spectrum of the driven atom.
We discuss the interaction of an atom subject to an intense driving laser field with its own radiation field. In contrast to the states of bare atoms, the energy difference between some dressed states with the same total angular momentum, its projection and parity may be very small. The self-interaction of a combined atom–laser system associated with nonradiative transitions between such states is effectively strong. We show that the contribution to the radiative shift of the sidebands of the Mollow spectrum, which comes from such processes, is very significant and may be much larger than the trivial Lamb shift, which is the simple redistribution of the Lamb shifts of the corresponding bare states. In the final part, we discuss the possibility that in the Mollow spectrum nonlocality of electromagnetic interaction, which in other cases is hidden in the regularization and renormalization procedures, can manifest itself explicitly.
It is known that the electromagnetic vacuum is responsible for the Lamb shift, which is a crucial phenomenon in quantum electrodynamics (QED). In circuit QED, the readout or bus resonators that are dispersively coupled can result in a significant Lamb shift of the qubit. However, previous approaches or proposals for controlling the Lamb shift in circuit QED demand overheads in circuit designs or non-perturbative renormalization of the system’s eigenbases, which can impose formidable limitations. In this work, we propose and demonstrate an all-microwave method for controlling the Lamb shift of fixed-frequency transmons. We employ the drive-induced longitudinal coupling between the transmon and resonator. By simply using an off-resonant monochromatic drive near the resonator frequency, we can control the net Lamb shift up to ±30 MHz and engineer it to zero with the drive-induced longitudinal coupling without facing the aforementioned challenges. Our work establishes an efficient way of engineering the fundamental effects of the electromagnetic vacuum and provides greater flexibility in non-parametric frequency controls of multilevel systems. Engineering the Lamb shifts of superconducting qubits opens new opportunities in resonant frequency tunings and other applications. Here, the authors devise and demonstrate an all-microwave approach that can be utilized with fixed-frequency superconducting qubits.
The authors present analytical and numerical results for resonance fluorescence produced by a two-level atom damped by a broad-band squeezed vacuum. Previous theoretical analyses of this model have assumed that the laser frequency and the carrier frequency of the squeezed vacuum are equal. The authors introduce a non-zero detuning between the laser frequency and the carrier frequency while maintaining resonance between the laser frequency and atomic resonance. In the absence of the driving field there is a squeezing threshold: above threshold the decay rate of the atomic polarization can be reduced, and below threshold a squeezing-induced two peak spectrum and frequency shift, which is analogous to the Bloch-Siegert shift, are predicted. In the presence of the driving field, the spectrum is asymmetric for Rabi frequencies smaller or comparable to the detuning of the squeezed vacuum. A symmetric spectrum is obtained for large Rabi frequencies. An interpretation is predicted by means of a dressed-state analysis. The authors find that for not too large Rabi frequencies a remarkably large population inversion can be induced in the dressed states, even at exact resonance of the driving field, provided that the laser frequency and carrier frequency are detuned. Moreover, for detection times larger than the inverse detuning, the spectrum is insensitive to the phase between the driving field and the squeezed vacuum, in marked contrast to the case of no detuning.
Quantum interference and coherence lead to many interesting phenomenon and applications in quantum optics. In this dissertation, we study the quantum coherent properties in the following systems and aspects. We first investigate the optical bistability in a combined cavity-cold atoms system. In such a system the atom-photon interaction provides an optical lattice to the atoms and affects the mechanical motion of the atoms while atoms induce a position dependent phase shift on the cavity field. This highly nonlinearity induces optical bistability of intra-cavity photon number with respect to the pumping light added along the cavity axis. We show that the presence of this bistability can be controlled by a second pumping field added perpendicular to the cavity axis. It is also found that the critical input intensity of switching from one branch of bistability to the other depends on the the way of the field being added. This behavior is similar to the anomalous switching of the dispersive optical bistability of atomic media in the cavity. We also study the effect of counter-rotating terms in the control of spontaneous emission. We make use of a unitary transformation method and investigate the effect of dynamic energy shifts on the spontaneous emission modification via quantum interference in a four-level atomic system. We show that the counter-rotating terms, which are normally neglected in the usual investigation of atomic systems, do produce a significant influence on the evolution of the atomic amplitudes and the emission spectrum. This effect of counter-rotating terms can be observed in the time scale of the decay rate even when the dipole moments of the two upper levels are orthogonal to each other. The effect of counter-rotating terms on the spontaneous emission in a 3-D anisotropic photonic crystal is also discussed. It is shown that the behavior of the emission is similar to the case making rotating wave approximation, i.e., the localized and propagating fields are also separated by two characteristic atomic transition frequencies. However, the two characteristic frequencies are shifted due to the full Lamb shift which is obtained with counter-rotating terms being included in the Hamiltonian. We also utilize the unitary transformation method to show how the Lamb shift in a multi-level atom can be controlled by a driving field. Finally, we propose a subwavelength atom localization scheme for an atom located in a standing-wave field. The strategy is based on the observation that the photon statistics of resonance fluorescence depends on the position-dependent Rabi frequency.