Quantum chaos and fractals with atoms in cavities

We study the coupled translational, electronic, and field dynamics of the combined system “a two-level atom + a single-mode quantized field + a standing-wave ideal cavity”. In the semiclassical approximation with a point-like atom, interacting with the classical field, the dynamics is described by the Heisenberg equations for the atomic and field expectation values which are known to produce semiclassical chaos under appropriate conditions. We derive Hamilton–Schrödinger equations for probability amplitudes and averaged position and momentum of a point-like atom interacting with the quantized field in a standing-wave cavity. They constitute, in general, an infinite-dimensional set of equations with an infinite number of integrals of motion which may be reduced to a dynamical system with four degrees of freedom if the quantized field is supposed to be initially prepared in a Fock state. This system is found to produce semiquantum chaos with positive values of the maximal Lyapunov exponent. At exact resonance, the semiquantum dynamics is regular. At large values of detuning |δ|1, the Rabi atomic oscillations are usually shallow, and the dynamics is found to be almost regular. The Doppler–Rabi resonance, deep Rabi oscillations that may occur at any large value of |δ| to be equal to |αp₀|, is found numerically and described analytically (with α to be the normalized recoil frequency and p₀ the initial atomic momentum). Two gedanken experiments are proposed to detect manifestations of semiquantum chaos in real experiments. It is shown that in the chaotic regime values of the population inversion z_out, measured with atoms after transversing a cavity, are so sensitive to small changes in the initial inversion z_in that the probability of detecting any value of z_out in the admissible interval [−1,1] becomes almost unity in a short time. Chaotic wandering of a two-level atom in a quantized Fock field is shown to be fractal. Fractal-like structures, typical with chaotic scattering, are numerically found in the dependence of the time of exit of atoms from the cavity on their initial momenta.     

Quantum electrodynamic effects in atomic structure

Summary In high-Z atoms, quantum electrodynamic (QED) corrections are an important component in the theoretical prediction of atomic energy levels. The main QED effects in electronic atoms are the one-electron self-energy and vacuum-polarization corrections which are well known. At the next level of precision, estimates of the effect of electron interactions on the self energy and higher-order effects in two exchanged photon corrections are necessary. These corrections can be evaluated within the framework of QED in the bound interaction picture. For high-Z few-electron atoms, this approach provides a rapidly converging series in 1/Z for the corrections, which is the generalization of the well-known relativistic 1/Z expansion methods. This paper describes recent work on the effect of electron interactions on the self energy. The QED effects are particularly important for the theory for lithiumlike uranium where an accurate measurement of the Lamb shift has been made, as well as for numerous other cases where systematic differences appear between theory that does not include these QED effects and experiment.     

Sustained photon pulse revivals from inhomogeneously broadened spin ensembles

A very promising recent trend in applied quantum physics is to combine the advantageous features of different quantum systems into what is called “hybrid quantum technology”. One of the key elements in this new field will have to be a quantum memory enabling to store quanta over extended periods of time. Systems that may fulfill the demands of such applications are comb‐shaped spin ensembles coupled to a cavity. Due to the decoherence induced by the inhomogeneous ensemble broadening, the storage time of these quantum memories is, however, still rather limited. Here we demonstrate how to overcome this problem by burning well‐placed holes into the spectral spin density leading to spectacular performance in the multimode regime. Specifically, we show how an initial excitation of the ensemble leads to the emission of more than a hundred well‐separated photon pulses with a decay rate significantly below the fundamental limit of the recently proposed “cavity protection effect”.

     

Scheme to Implement Optimal Asymmetric Economical Phase-Covariant Quantum Cloning in Cavity QED

We propose an experimentally feasible scheme to implement the optimal asymmetric economical 1→2 phase-covariant quantum cloning in two dimensions based on the cavity QED technique. The protocol is very simple and only two atoms are required. Our scheme is insensitive to the cavity field states and cavity decay. During the processes, the cavity is only virtually excited and it thus greatly prolongs the efficient decoherent time. Therefore, it may be realized in experiment.     

Recent research using the Oxford electron beam ion trap

The presence of the σ-phase in Fe-Cr alloys (eg. Stainless steel) is important in industrial applications and from an academic point of view. The presence of the σ-phase in these alloys drastically affects their mechanical properties and their resistance to various corrosive media. In the present investigation Fe-Cr alloys containing different amounts of Mo were prepared and the transformation to the σ-phase was carried out by isothermally annealing the samples for various periods in an argon atmosphere. It will be shown that the presence of Mo has a dramatic accelerating effect on the rate of the σ-phase formation in these alloys. This revised version was published online in August 2006 with corrections to the Cover Date.     

Construction of the ground state in nonrelativistic QED by continuous flows

For a nonrelativistic hydrogen atom minimally coupled to the quantized radiation field we construct the ground state projection Pgs by a continuous approximation scheme as an alternative to the iteration scheme recently used by Fröhlich, Pizzo, and the first author [V. Bach, J. Fröhlich, A. Pizzo, Infrared-finite algorithms in QED: The groundstate of an atom interacting with the quantized radiation field, Comm. Math. Phys. (2006), doi: 10.1007/s00220-005-1478-3]. That is, we construct Pgs=limt→∞Pt as the limit of a continuously differentiable family (Pt)_t?0 of ground state projections of infrared regularized Hamiltonians Ht. Using the ODE solved by this family of projections, we show that the norm of their derivative is integrable in t which in turn yields the convergence of Pt by the fundamental theorem of calculus.     

Scheme for implementing quantum dense coding with W-class state in cavity QED

An experimentally feasible protocol for realizing dense coding by using a class of W-state in cavity quantum electrodynamics （QED） is proposed in this paper. The prominent advantage of our scheme is that the successful probability of the dense coding with a W-class state can reach 1. In addition, the scheme can be implemented by the present cavity QED techniques.     

Cavity QED based tuneable,delayed-choice quantum eraser

We propose an experimentally feasible idea for the delayed-choice quantum eraser, having adjustable path distinguishability/fringe visibility. The schematics are based on resonant, dispersive and Ramsey interactions of atoms under cavity QED scenario. The option for tuneability of the fringes in a delayed-choice setup stringently marks the conception of the time in the quantum theory, operational meanings of the state vector reduction and raises questions about Ψ$\Psi$-ontic models while helping to shed out the controversies surrounding the quantum eraser theme. The proposal can be efficiently executed experimentally within the prevailing cavity QED experimental research scenario with good overall success probability and fidelity.     

Implementation of Controlled‐NOT Gate by Lyapunov Control

A scheme to implement the controlled‐NOT (CNOT) gate for quantum systems is proposed, which is based on Lyapunov control. The scheme does not require precise control of the interaction time since the system is stable when the control fields vanish. In particular, the control fields can be easily obtained by most initial states. As an example, the CNOT gate is realized for two atoms trapped in an optical cavity by exploiting two disturbance cases. Compared to continuous disturbance, the fidelity of the CNOT gate is higher under impulsive disturbance, however, interaction times are much longer. Numerical simulations indicate that the scheme is robust against variations of control parameters and decoherence caused by atomic spontaneous emission and cavity decay. Therefore, the scheme may provide useful applications in quantum computation.     

One-step implementation of a multi-target-qubit controlled phase gate with cat-state qubits in circuit QED

We propose a single-step implementation of a muti-target-qubit controlled phase gate with one catstate qubit (cqubit) simultaneously controlling n–1 target cqubits. The two logic states of a cqubit are represented by two orthogonal cat states of a single cavity mode. In this proposal, the gate is implemented with n microwave cavities coupled to a superconducting transmon qutrit. Because the qutrit remains in the ground state during the gate operation, decoherence caused due to the qutrit’s energy relaxation and dephasing is greatly suppressed. The gate implementation is quite simple because only a single-step operation is needed and neither classical pulse nor measurement is required. Numerical simulations demonstrate that high-fidelity realization of a controlled phase gate with one cqubit simultaneously controlling two target cqubits is feasible with present circuit QED technology. This proposal can be extended to a wide range of physical systems to realize the proposed gate, such as multiple microwave or optical cavities coupled to a natural or artificial three-level atom.