Quantum feedback control of a solid-state qubit

We have studied theoretically the basic operation of a quantum feedback loop designed to maintain a desired phase of quantum coherent oscillations in a single solid-state qubit. The degree of oscillations synchronization with external harmonic signal is calculated as a function of feedback strength, taking into account available bandwidth and coupling to environment. The feedback can efficiently suppress the dephasing of oscillations if the qubit coupling to the detector is stronger than coupling to environment.Comment: Extended version of cond-mat/0107280 (5 pages, 5 figures); to be published in PRB (RC

Cooling of a single atom in an optical trap inside a resonator

We present detailed discussions of cooling and trapping mechanisms for an atom in an optical trap inside an optical cavity, as relevant to recent experiments. The interference pattern of cavity QED and trapping fields in space makes the trapping wells distinguishable from one another. This adds considerable flexibility to creating effective trapping and cooling conditions and to detection possibilities. Friction and diffusion coefficients are calculated in and beyond the low excitation limit and full 3-D simulations of the quasiclassical motion of a Cs atom are performed.Comment: One more figure and one more autho

Sensitivity optimization in quantum parameter estimation

We present a general framework for sensitivity optimization in quantum parameter estimation schemes based on continuous (indirect) observation of a dynamical system. As an illustrative example, we analyze the canonical scenario of monitoring the position of a free mass or harmonic oscillator to detect weak classical forces. We show that our framework allows the consideration of sensitivity scheduling as well as estimation strategies for non-stationary signals, leading us to propose corresponding generalizations of the Standard Quantum Limit for force detection.Comment: 15 pages, RevTe

Feedback cooling of a nanomechanical resonator

Cooled, low-loss nanomechanical resonators offer the prospect of directly observing the quantum dynamics of mesoscopic systems. However, the present state of the art requires cooling down to the milliKelvin regime in order to observe quantum effects. Here we present an active feedback strategy based on continuous observation of the resonator position for the purpose of obtaining these low temperatures. In addition, we apply this to an experimentally realizable configuration, where the position monitoring is carried out by a single-electron transistor. Our estimates indicate that with current technology this technique is likely to bring the required low temperatures within reach.Comment: 10 pages, RevTex4, 4 color eps figure

Cavity QED and quantum information processing with "hot" trapped atoms

We propose a method to implement cavity QED and quantum information processing in high-Q cavities with a single trapped but non-localized atom. The system is beyond the Lamb-Dick limit due to the atomic thermal motion. Our method is based on adiabatic passages, which make the relevant dynamics insensitive to the randomness of the atom position with an appropriate interaction configuration. The validity of this method is demonstrated from both approximate analytical calculations and exact numerical simulations. We also discuss various applications of this method based on the current experimental technology.Comment: 14 pages, 8 figures, Revte

Constructing Entanglement Witness Via Real Skew-Symmetric Operators

In this work, new types of EWs are introduced. They are constructed by using real skew-symmetric operators defined on a single party subsystem of a bipartite dxd system and a maximal entangled state in that system. A canonical form for these witnesses is proposed which is called canonical EW in corresponding to canonical real skew-symmetric operator. Also for each possible partition of the canonical real skew-symmetric operator corresponding EW is obtained. The method used for dxd case is extended to d1xd2 systems. It is shown that there exist Cd2xd1 distinct possibilities to construct EWs for a given d1xd2 Hilbert space. The optimality and nd-optimality problem is studied for each type of EWs. In each step, a large class of quantum PPT states is introduced. It is shown that among them there exist entangled PPT states which are detected by the constructed witnesses. Also the idea of canonical EWs is extended to obtain other EWs with greater PPT entanglement detection power.Comment: 40 page

Efficient measurements, purification, and bounds on the mutual information

When a measurement is made on a quantum system in which classical information is encoded, the measurement reduces the observers average Shannon entropy for the encoding ensemble. This reduction, being the {\em mutual information}, is always non-negative. For efficient measurements the state is also purified; that is, on average, the observers von Neumann entropy for the state of the system is also reduced by a non-negative amount. Here we point out that by re-writing a bound derived by Hall [Phys. Rev. A {\bf 55}, 100 (1997)], which is dual to the Holevo bound, one finds that for efficient measurements, the mutual information is bounded by the reduction in the von Neumann entropy. We also show that this result, which provides a physical interpretation for Hall's bound, may be derived directly from the Schumacher-Westmoreland-Wootters theorem [Phys. Rev. Lett. {\bf 76}, 3452 (1996)]. We discuss these bounds, and their relationship to another bound, valid for efficient measurements on pure state ensembles, which involves the subentropy.Comment: 4 pages, Revtex4. v3: rewritten and reinterpreted somewha

Information dynamics in cavity QED

A common experimental setup in cavity quantum electrodynamics (QED) consists of a single two-level atom interacting with a single mode of the electromagnetic field inside an optical cavity. The cavity is externally driven and the output is continuously monitored via homodyne measurements. We derive formulas for the optimal rates at which these measurements provide information about (i) the quantum state of the system composed of atom and electromagnetic field, and (ii) the coupling strength between atom and field. We find that the two information rates are anticorrelated.Comment: 11 pages, 1 figure, final versio

Mirror quiescence and high-sensitivity position measurements with feedback

We present a detailed study of how phase-sensitive feedback schemes can be used to improve the performance of optomechanical devices. Considering the case of a cavity mode coupled to an oscillating mirror by the radiation pressure, we show how feedback can be used to reduce the position noise spectrum of the mirror, cool it to its quantum ground state, or achieve position squeezing. Then, we show that even though feedback is not able to improve the sensitivity of stationary position spectral measurements, it is possible to design a nonstationary strategy able to increase this sensitivity.Comment: 25 pages, 11 figure

Continuous Quantum Measurement and the Quantum to Classical Transition

While ultimately they are described by quantum mechanics, macroscopic mechanical systems are nevertheless observed to follow the trajectories predicted by classical mechanics. Hence, in the regime defining macroscopic physics, the trajectories of the correct classical motion must emerge from quantum mechanics, a process referred to as the quantum to classical transition. Extending previous work [Bhattacharya, Habib, and Jacobs, Phys. Rev. Lett. {\bf 85}, 4852 (2000)], here we elucidate this transition in some detail, showing that once the measurement processes which affect all macroscopic systems are taken into account, quantum mechanics indeed predicts the emergence of classical motion. We derive inequalities that describe the parameter regime in which classical motion is obtained, and provide numerical examples. We also demonstrate two further important properties of the classical limit. First, that multiple observers all agree on the motion of an object, and second, that classical statistical inference may be used to correctly track the classical motion.Comment: 12 pages, 4 figures, Revtex