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arXiv:0710.1075 · Physical Review A

Fine tuning of quantum operations performed via Raman transitions

Grzegorz Chimczak, R. Tanaś

Published Mar 7, 2008• 7 citations
arXivHTMLPDF

Abstract

A scheme for fine tuning of quantum operations to improve their performance is proposed. A quantum system in $\ensuremath{\Lambda}$ configuration with two-photon Raman transitions is considered without adiabatic elimination of the excited (intermediate) state. Conditional dynamics of the system is studied with focus on improving fidelity of quantum operations. In particular, the $\ensuremath{\pi}$ pulse and $\ensuremath{\pi}∕2$ pulse quantum operations are considered. The dressed states for the atom-field system, with an atom driven on one transition by a classical field and on the other by a quantum cavity field, are found. A discrete set of detunings is given for which high fidelity of desired states is achieved. Analytical solutions for the quantum state amplitudes are found in the first order perturbation theory with respect to the cavity damping rate $\ensuremath{\kappa}$ and the spontaneous emission rate $\ensuremath{\gamma}$. Numerical solutions for higher values of $\ensuremath{\kappa}$ and $\ensuremath{\gamma}$ indicate a stabilizing role of spontaneous emission in the $\ensuremath{\pi}$ and $\ensuremath{\pi}∕2$ pulse quantum operations. The idea can also be applied for excitation pulses of different shapes.

DOI
10.1103/physreva.77.032312

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A scheme for fine tuning of quantum operations to improve their performance is proposed. A quantum system in \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ configuration with two-photon Raman transitions is considered without adiabatic elimination of the excited (intermediate) state. Conditional dynamics of the system is studied with focus on improving fidelity of quantum operations. In particular, the \ensuremathπ\ensuremath{\pi}\ensuremathπ pulse and \ensuremathπ∕2\ensuremath{\pi}∕2\ensuremathπ∕2 pulse quantum operations are considered. The dressed states for the atom-field system, with an atom driven on one transition by a classical field and on the other by a quantum cavity field, are found. A discrete set of detunings is given for which high fidelity of desired states is achieved. Analytical solutions for the quantum state amplitudes are found in the first order perturbation theory with respect to the cavity damping rate \ensuremathκ\ensuremath{\kappa}\ensuremathκ and the spontaneous emission rate \ensuremathγ\ensuremath{\gamma}\ensuremathγ. Numerical solutions for higher values of \ensuremathκ\ensuremath{\kappa}\ensuremathκ and \ensuremathγ\ensuremath{\gamma}\ensuremathγ indicate a stabilizing role of spontaneous emission in the \ensuremathπ\ensuremath{\pi}\ensuremathπ and \ensuremathπ∕2\ensuremath{\pi}∕2\ensuremathπ∕2 pulse quantum operations. The idea can also be applied for excitation pulses of different shapes.
Dynamic coupling of cavities to a quantum network is of major interest to distributed quantum information processing schemes based on cavity quantum electrodynamics. This can be achieved by actively tuning a mediating atom-cavity system. In particular, we consider the dynamic coupling between two coupled cavities, each interacting with a two-level atom, realized by tuning one of the atoms. One atom-field system can be controlled to become maximally and minimally coupled with its counterpart, allowing high fidelity excitation confinement, QQQ switching, and reversible state transport. As an application, we first show that simple tuning can lead to emission of near-Gaussian single-photon pulses that is significantly different from the usual exponential decay in a passive cavity-based system. The influences of cavity loss and atomic spontaneous emission are studied in detailed numerical simulations, showing the practicality of these schemes within the reach of current experimental solid-state technology. We then show that when the technique is employed to an extended coupled-cavity scheme involving a multilevel atom, arbitrary temporal superposition of single photons can be engineered in a deterministic way.
We demonstrate that in stimulated Raman transitions introducing one or two simple phase shifts to the control fields significantly enhances the fidelity of state manipulation while simultaneously reducing leakage to the intermediate excited state. Our approach achieves high-fidelity quantum gate operations between the two target states under arbitrary detuning conditions. Notably, the average population in the intermediate excited state is approximately halved, without extending the overall evolution time. Additionally, our method exhibits greater robustness to static amplitude and detuning errors compared to conventional adiabatic elimination techniques, and maintains higher fidelity even in the presence of dissipation.
Single photon source is one of the key devices for optical quantum information processings. Differing from the usual method to obtain single-photon radiations by using the spontaneous emissions of \pi-pulse excited atoms, here we propose an approach to produce optical Fock states on demand in the usual atom-cavity system by utilizing the technique of shortcuts to adiabatic passages.It is shown that, by applying auxiliary pulse(s) (besides the usual pumps to excite atom in the cavity), the desirable transitionless quantum drivings for Fock state productions (FSPs) could be implemented deterministically.Compared with the previous method based on stimulated Raman adiabatic passages for the FSPs [see, e.g., A. S. Parkins et. al., Phys. Rev. Lett. 71, 3095 (1993) for theoretical proposal; and A. Kuhn et. al., Phys. Rev. Lett. 89, 067901 (2002) for experimental demonstrations], the present proposal suppress effectively the unwanted but practically unavoidable nonadiabatic transitions in the previous schemes during the drivings. Therefore, the efficiency of FSPs by the present technique should be significantly high, even in the presence of various atomic and cavity dissipations.
Taking the non-Markovian effect into account, we study how to store a single photon of arbitrary temporal shape in a single atom coupled to an optical cavity. Our model applies to Raman transitions in three-level atoms, with one branch of the transition controlled by a driving pulse, and the other coupled to the cavity. For any couplings of input field to the optical cavity and detunings of the atom from the driving pulse and cavity, we extend the input-output relation from Markovian to non-Markovian dynamics. For most possible photon shapes, we derive an analytic expression for the driving pulse in order to completely map the input photon into the atom. We find that the amplitude of the driving pulse depends only on the detuning of the atom from the frequency of the cavity, i.e., the detuning of the atom to the driving pulse has no effect on the strength of the driving pulse.
Stimulated Raman interaction of a classically pumped single three-level ΛΛΛ-type atom in a resonator cavity featuring both radiative and unwanted losses is studied. It is shown that in the regime of stimulated adiabatic Raman passage the excited outgoing wave packet of the cavity-assisted electromagnetic field can be prepared in a one-photon Fock state with high efficiency. In this regime, the spatio-temporal shape of the wave packet does not depend on the interaction shape of the pump field, provided that the interaction of the atom with the pump is time-delayed with respect to the interaction of the atom with the cavity-assisted field. Therefore, the scheme can be used to generate a sequence of identical radiation pulses each of almost one-photon Fock state. It is further shown that the spatio-temporal shape of the outgoing wave packet can be manipulated by controlling the time of interaction between the atom and the cavity-assisted electromagnetic field.
In order to study quantum effects such as state superposition and entanglement, one would like to construct simple systems for which the damping rates are slow relative to the rate of coherent evolution. One such system is strong-coupling cavity quantum electrodynamics (QED), in which a single atom is coupled to a single mode of a high finesse optical cavity. In recent years, optical trapping techniques have been applied to the cavity QED system, allowing an individual atom to remain coupled to the cavity for long periods of time. For the purpose of future cavity QED experiments, one would like to gain as much control over the trapped atom as possible; in particular, one would like to cool the center of mass motion of the atom, to measure the magnetic field at the location of the atom, and to be able to prepare the atom in a given internal state. In the first part of this thesis, I present a scheme for driving Raman transitions inside the cavity that can be used to achieve these goals. After giving a detailed theoretical treatment of the Raman scheme, I describe how it can be implemented in the lab and discuss some preliminary experimental results. In the second part of this thesis, I present a number of simple field theory models. These models were developed in an attempt to understand some of the central ideas of theoretical physics by looking at how the ideas work in a highly simplified context. The hope is that by reducing the mathematical complexity of an actual theory, the underlying physical concepts can be more easily understood.