Two-photon detuning and decoherence in cavity electromagnetically induced transparency for quantized fields

The interaction of a quantized field with three-level atoms in $\Lambda$ configuration inside a two-mode cavity is analyzed in the small noise approximation. The atoms are in a two-photon detuning with respect to the carriers of the field. We calculate the stationary quadrature noise spectrum of the field outside the cavity in the case where the input probe field is a squeezed state and the input pump field is a coherent state. The mean value of the field is unaltered in all the analysis: the atoms shows electromagnetically induced transparency (EIT). The effect of the atoms' base level decoherence in the cavity output field is also studied. It is found that the output field is very sensitive to two-photon detuning.Comment: 8 page

Noncovariant gauge fixing in the quantum Dirac field theory of atoms and molecules

Starting from the Weyl gauge formulation of quantum electrodynamics (QED), the formalism of quantum-mechanical gauge fixing is extended using techniques from nonrelativistic QED. This involves expressing the redundant gauge degrees of freedom through an arbitrary functional of the gauge-invariant transverse degrees of freedom. Particular choices of functional can be made to yield the Coulomb gauge and Poincar\'{e} gauge representations. The Hamiltonian we derive therefore serves as a good starting point for the description of atoms and molecules by means of a relativistic Dirac field. We discuss important implications for the ontology of noncovariant canonical QED due to the gauge freedom that remains present in our formulation.Comment: 8 pages, 0 figure

Coherent pumping of a Mott insulator: Fermi golden rule versus Rabi oscillations

Cold atoms provide a unique arena to study many-body systems far from equilibrium. Furthermore, novel phases in cold atom systems are conveniently investigated by dynamical probes pushing the system out of equilibrium. Here, we discuss the pumping of doubly-occupied sites in a fermionic Mott insulator by a periodic modulation of the hopping amplitude. We show that deep in the insulating phase the many-body system can be mapped onto an effective two-level system which performs coherent Rabi oscillations due to the driving. Coupling the two-level system to the remaining degrees of freedom renders the Rabi oscillations damped. We compare this scheme to an alternative description where the particles are incoherently pumped into a broad continuum.Comment: 4 pages, 3 figure

Storage of classical information in quantum spins

Digital magnetic recording is based on the storage of a bit of information in the orientation of a magnetic system with two stable ground states. Here we address two fundamental problems that arise when this is done on a quantized spin: quantum spin tunneling and back-action of the readout process. We show that fundamental differences exist between integer and semi-integer spins when it comes to both, read and record classical information in a quantized spin. Our findings imply fundamental limits to the miniaturization of magnetic bits and are relevant to recent experiments where spin polarized scanning tunneling microscope reads and records a classical bit in the spin orientation of a single magnetic atom

State-dependent rotations of spins by weak measurements

IIt is shown that a weak measurement of a quantum system produces a new state of the quantum system which depends on the prior state, as well as the (uncontrollable) measured position of the pointer variable of the weak measurement apparatus. The result imposes a constraint on hidden-variable theories which assign a different state to a quantum system than standard quantum mechanics. The constraint means that a crypto-nonlocal hidden-variable theory can be ruled out in a more direct way than previously.Comment: 10 pages, 2 figures. Substantially revised to concentrate on weak measurement transformation of states and application to crypto-nonlocal hidden-variable theor

Extension of the Huttner-Barnett model to a magnetodielectric medium

The Huttner$-$Barnett model is extended to a magnetodielectric medium by adding a new matter field to this model. The eigenoperators for the coupled system are calculated and electromagnetic field is written in terms of these operators. The electric and magnetic susceptibility of the medium are explicitly derived and shown to satisfy the Kramers$-$Kronig relations. It is shown that the results obtained in this model are equivalent to the results obtained from the phenomenological methods.Comment: 25 page

Limits of sympathetic cooling of fermions by zero temperature bosons due to particle losses

It has been suggested by Timmermans [Phys. Rev. Lett. {\bf 87}, 240403 (2001)] that loss of fermions in a degenerate system causes strong heating. We address the fundamental limit imposed by this loss on the temperature that may be obtained by sympathetic cooling of fermions by bosons. Both a quantum Boltzmann equation and a quantum Boltzmann \emph{master} equation are used to study the evolution of the occupation number distribution. It is shown that, in the thermodynamic limit, the Fermi gas cools to a minimal temperature $k_{{\rm B}}T/\mu\propto(\gamma_{{\rm loss}}/\gamma_{{\rm coll}})^{0.44}$, where $\gamma_{{\rm loss}}$ is a constant loss rate, $\gamma_{{\rm coll}}$ is the bare fermion--boson collision rate not including the reduction due to Fermi statistics, and $\mu\sim k_{{\rm B}}T_{{\rm F}}$ is the chemical potential. It is demonstrated that, beyond the thermodynamic limit, the discrete nature of the momentum spectrum of the system can block cooling. The unusual non-thermal nature of the number distribution is illustrated from several points of view: the Fermi surface is distorted, and in the region of zero momentum the number distribution can descend to values significantly less than unity. Our model explicitly depends on a constant evaporation rate, the value of which can strongly affect the minimum temperature.Comment: 14 pages, 7 figures. Phys. Rev. A in pres

Control of dipolar relaxation in external fields

We study dipolar relaxation in both ultra-cold thermal and Bose-condensed chromium atom gases. We show three different ways to control dipolar relaxation, making use of either a static magnetic field, an oscillatory magnetic field, or an optical lattice to reduce the dimensionality of the gas from 3D to 2D. Although dipolar relaxation generally increases as a function of a static magnetic field intensity, we find a range of non-zero magnetic field intensities where dipolar relaxation is strongly reduced. We use this resonant reduction to accurately determine the S=6 scattering length of chromium atoms: $a_6 = 103 \pm 4 a_0$. We compare this new measurement to another new determination of $a_6$, which we perform by analysing the precise spectroscopy of a Feshbach resonance in d-wave collisions, yielding $a_6 = 102.5 \pm 0.4 a_0$. These two measurements provide by far the most precise determination of $a_6$ to date. We then show that, although dipolar interactions are long-range interactions, dipolar relaxation only involves the incoming partial wave $l=0$ for large enough magnetic field intensities, which has interesting consequences on the stability of dipolar Fermi gases. We then study ultra-cold chromium gases in a 1D optical lattice resulting in a collection of independent 2D gases. We show that dipolar relaxation is modified when the atoms collide in reduced dimensionality at low magnetic field intensities, and that the corresponding dipolar relaxation rate parameter is reduced by a factor up to 7 compared to the 3D case. Finally, we study dipolar relaxation in presence of radio-frequency (rf) oscillating magnetic fields, and we show that both the output channel energy and the transition amplitude can be controlled by means of rf frequency and Rabi frequency.Comment: 25 pages, 17 figure

Non-Local Quantum Gates: a Cavity-Quantum-Electro-Dynamics implementation

The problems related to the management of large quantum registers could be handled in the context of distributed quantum computation: unitary non-local transformations among spatially separated local processors are realized performing local unitary transformations and exchanging classical communication. In this paper, we propose a scheme for the implementation of universal non-local quantum gates such as a controlled-\gate{NOT} (\cnot) and a controlled-quantum phase gate (\gate{CQPG}). The system we have chosen for their physical implementation is a Cavity-Quantum-Electro-Dynamics (CQED) system formed by two spatially separated microwave cavities and two trapped Rydberg atoms. We describe the procedures to follow for the realization of each step necessary to perform a specific non-local operation.Comment: 12 pages, 5 figures, RevTeX; extensively revised versio

Lamb Shift of Laser-Dressed Atomic States

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.Comment: 4 pages, 1 figure, submitted for publicatio