Minimum-energy pulses for quantum logic cannot be shared

J. Gea-Banacloche and Masanao Ozawa

We show that if an electromagnetic energy pulse with average photon number n is used to carry out the same quantum logical operation on a set of N atoms, either simultaneously or sequentially, the overall error probability in the worst case scenario (i.e., maximized over all the possible initial atomic states) scales as N²/n. This means that in order to keep the error probability bounded by Nε, with ε ~ 1/n, one needs to use Nn photons, or equivalently N separate "minimum-energy" pulses: in this sense the pulses cannot, in general, be shared. The origin for this phenomenon is found in atom-field entanglement. These results may have important consequences for quantum logic and, in particular, for large-scale quantum computation.

Submitted to Phys. Rev. Lett. preprint

Optical switching in arrays of quantum dots with dipole-dipole interactions

J. Gea-Banacloche, Mambwe Mumba and Min Xiao

We explore the possibility of using pairs of quantum dots coupled by the dipole-dipole interaction as effective three- or four-level systems whose transmission for an optical beam at some frequency may be switched on or off using a second optical beam (electromagnetically-induced transparency). We conclude that the characteristic interaction strengths and decay rates should allow for a demonstration of this effect in MBE-grown bilayer InAs/GaAs quantum dot structures.

Submitted to Phys. Rev. B preprint

Adiabatic geometric phase gate with a quantized control field

Shabnam Siddiqui and Julio Gea-Banacloche

We study the performance of an adiabatic, geometric phase gate with a quantized driving field numerically, and develop an analytical approximation that shows how the qubit becomes entangled with the driving field. This results in a scaling of the gate error probability versus the energy in the control field that has the same form as that found for dynamic, nonadiabatic gates, but with a prefactor that would typically be several orders of magnitude larger, because of the adiabaticity constraint. In the approximation we have used, which should be valid for sufficiently large control fields, the main source of decoherence (and hence error) is the "which path" information carried by the photons that would be radiated by the driven qubit.

Submitted to Phys. Rev. A preprint

Steady State Entanglement in Cavity QED

P. R. Rice, J. Gea-Banacloche, M. L. Terraciano, D. L. Freimund, and L. A. Orozco

We investigate steady state entanglement in an open quantum system, specifically a single atom in a driven optical cavity with cavity loss and spontaneous emission. The system reaches a steady pure state when driven very weakly. Under these conditions, there is an optimal value for atom-field coupling to maximize entanglement, as larger coupling favors a loss port due to the cavity enhanced spontaneous emission. We address ways to implement measurements of entanglement witnesses and find that normalized cross-correlation functions are indicators of the entanglement in the system. The magnitude of the equal time intensity-field cross correlation between the transmitted field of the cavity and the fluorescence intensity is proportional to the concurrence for weak driving fields.

Optics Express 14, Issue 10, pp. 4514-4524 (May 2006) direct link

Two-reservoir model of quantum error correction

James P. Clemens and J. Gea-Banacloche

We consider a two-reservoir model of quantum error correction with a hot bath causing errors in the qubits and a cold bath cooling the ancilla qubits to a fiducial state. We consider error correction protocols both with and without measurement of the ancilla state. The error correction acts as a kind of refrigeration process to maintain the data qubits in a low entropy state by periodically moving the entropy to the ancilla qubits and then to the cold reservoir. We quantify the performance of the error correction as a function of the reservoir temperatures and cooling rate by means of the fidelity and the residual entropy of the data qubits. We also make a comparison with the continuous quantum error correction model of Sarovar and Milburn [Phys. Rev. A 72, 012306 (2005)].

Phys. Rev. A 73, 022337 (2006) (10 pages) direct link

Quantum version of the szilard one-atom engine and the cost of raising energy barriers

Julio Gea-Banacloche and Harvey S. Leff

We present a variation on the Szilard one-atom engine ``paradox,'' in which an adiabatic (in the quantum-mechanical sense) splitting of the container removes the need for a demon or measurement. We show that the solution depends on an interesting difference between the energetic cost of raising partitions in quantum and classical containers.

Fluctuations and Noise Letters, 5, no. 4, C39 (2005) indirect link

Effects of random localizing events on matter waves: formalism and examples

Julio Gea-Banacloche

A formalism is introduced to describe a number of physical processes that may break down the coherence of a matter wave over a characteristic length scale l. In a second-quantized description, an appropriate master equation for a set of bosonic "modes" (such as atoms in a lattice, in a tight-binding approximation) is derived. Two kinds of "localizing processes" are discussed in some detail and shown to lead to master equations of this general form: spontaneous emission, and modulation by external random potentials. Some of the dynamical consequences of these processes are considered: in particular, it is shown that they generically lead to a damping of the motion of the matter-wave currents, and may also cause a "flattening" of the density distribution of a trapped condensate at rest.

J. Phys. B: At. Mol. Opt. Phys. 39 (2006) 69-84. direct link

Mean-field treatment of the damping of the oscillations of a 1D Bose gas in an optical lattice

Julio Gea-Banacloche, Ana Maria Rey, Guido Pupillo, Carl J. Williams, and Charles W. Clark

We present a theoretical treatment of the surprisingly large damping observed recently in one-dimensional Bose-Einstein atomic condensates in optical lattices. We show that time-dependent Hartree-Fock-Bogoliubov (HFB) calculations can describe qualitatively the main features of the damping observed over a range of lattice depths. We also derive a formula of the fluctuation-dissipation type for the damping, based on a picture in which the coherent motion of the condensate atoms is disrupted as they try to flow through the random local potential created by the irregular motion of noncondensate atoms. When parameters for the characteristic strength and correlation times of the fluctuations, obtained from the HFB calculations, are substituted in the damping formula, we find very good agreement with the experimentally-observed damping, as long as the lattice is shallow enough for the fraction of atoms in the Mott insulator phase to be negligible. We also include, for completeness, the results of other calculations based on the Gutzwiller ansatz, which appear to work better for the deeper lattices.

Phys. Rev. A 73, 013605 (2006) (9 pages) direct link

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