Cat States and Single Runs for the Damped Harmonic Oscillator

We discuss the fate of initial states of the cat type for the damped harmonic oscillator, mostly employing a linear version of the stochastic Schr\"odinger equation. We also comment on how such cat states might be prepared and on the relation of single realizations of the noise to single runs of experiments.Comment: 18, Revte

Heating and decoherence suppression using decoupling techniques

We study the application of decoupling techniques to the case of a damped vibrational mode of a chain of trapped ions, which can be used as a quantum bus in linear ion trap quantum computers. We show that vibrational heating could be efficiently suppressed using appropriate ``parity kicks''. We also show that vibrational decoherence can be suppressed by this decoupling procedure, even though this is generally more difficult because the rate at which the parity kicks have to applied increases with the effective bath temperature.Comment: 13 pages, 5 figures. Typos corrected, references adde

Targeting qubit states using open-loop control

We present an open-loop (bang-bang) scheme which drives an open two-level quantum system to any target state, while maintaining quantum coherence throughout the process. The control is illustrated by a realistic simulation for both adiabatic and thermal decoherence. In the thermal decoherence regime, the control achieved by the proposed scheme is qualitatively similar, at the ensemble level, to the control realized by the quantum feedback scheme of Wang, Wiseman, and Milburn [Phys. Rev. A 64, #063810 (2001)] for the spontaneous emission of a two-level atom. The performance of the open-loop scheme compares favorably against the quantum feedback scheme with respect to robustness, target fidelity and transition times.Comment: 27 pages, 7 figure

Physical interpretation of stochastic Schroedinger equations in cavity QED

We propose physical interpretations for stochastic methods which have been developed recently to describe the evolution of a quantum system interacting with a reservoir. As opposed to the usual reduced density operator approach, which refers to ensemble averages, these methods deal with the dynamics of single realizations, and involve the solution of stochastic Schr\"odinger equations. These procedures have been shown to be completely equivalent to the master equation approach when ensemble averages are taken over many realizations. We show that these techniques are not only convenient mathematical tools for dissipative systems, but may actually correspond to concrete physical processes, for any temperature of the reservoir. We consider a mode of the electromagnetic field in a cavity interacting with a beam of two- or three-level atoms, the field mode playing the role of a small system and the atomic beam standing for a reservoir at finite temperature, the interaction between them being given by the Jaynes-Cummings model. We show that the evolution of the field states, under continuous monitoring of the state of the atoms which leave the cavity, can be described in terms of either the Monte Carlo Wave-Function (quantum jump) method or a stochastic Schr\"odinger equation, depending on the system configuration. We also show that the Monte Carlo Wave-Function approach leads, for finite temperatures, to localization into jumping Fock states, while the diffusion equation method leads to localization into states with a diffusing average photon number, which for sufficiently small temperatures are close approximations to mildly squeezed states.Comment: 12 pages RevTeX 3.0 + 6 figures (GIF format; for higher-resolution postscript images or hardcopies contact the authors.) Submitted to Phys. Rev.

Non-Markovian quantum trajectories for spectral detection

We present a formulation of non-Markovian quantum trajectories for open systems from a measurement theory perspective. In our treatment there are three distinct ways in which non-Markovian behavior can arise; a mode dependent coupling between bath (reservoir) and system, a dispersive bath, and by spectral detection of the output into the bath. In the first two cases the non-Markovian behavior is intrinsic to the interaction, in the third case the non-Markovian behavior arises from the method of detection. We focus in detail on the trajectories which simulate real-time spectral detection of the light emitted from a localized system. In this case, the non-Markovian behavior arises from the uncertainty in the time of emission of particles that are later detected. The results of computer simulations of the spectral detection of the spontaneous emission from a strongly driven two-level atom are presented

Non-Markovian stochastic Schr\"odinger equations: Generalization to real-valued noise using quantum measurement theory

Do stochastic Schr\"odinger equations, also known as unravelings, have a physical interpretation? In the Markovian limit, where the system {\em on average} obeys a master equation, the answer is yes. Markovian stochastic Schr\"odinger equations generate quantum trajectories for the system state conditioned on continuously monitoring the bath. For a given master equation, there are many different unravelings, corresponding to different sorts of measurement on the bath. In this paper we address the non-Markovian case, and in particular the sort of stochastic \sch equation introduced by Strunz, Di\' osi, and Gisin [Phys. Rev. Lett. 82, 1801 (1999)]. Using a quantum measurement theory approach, we rederive their unraveling which involves complex-valued Gaussian noise. We also derive an unraveling involving real-valued Gaussian noise. We show that in the Markovian limit, these two unravelings correspond to heterodyne and homodyne detection respectively. Although we use quantum measurement theory to define these unravelings, we conclude that the stochastic evolution of the system state is not a true quantum trajectory, as the identity of the state through time is a fiction.Comment: 17 pages, 3 figure

Schroedinger cat-like states by conditional measurements on a beam-splitter

A scheme for generating Schr\"{o}dinger cat-like states of a single-mode optical field by means of conditional measurement is proposed. Feeding into a beam splitter a squeezed vacuum and counting the photons in one of the output channels, the conditional states in the other output channel exhibit a number of properties that are very similar to those of superpositions of two coherent states with opposite phases. We present analytical and numerical results for the photon-number and quadrature-component distributions of the conditional states and their Wigner and Husimi functions. Further, we discuss the effect of realistic photocounting on the states.Comment: 6 figures(divided in subfigures) using a4.st

Continuous quantum error correction via quantum feedback control

We describe a protocol for continuously protecting unknown quantum states from decoherence that incorporates design principles from both quantum error correction and quantum feedback control. Our protocol uses continuous measurements and Hamiltonian operations, which are weaker control tools than are typically assumed for quantum error correction. We develop a cost function appropriate for unknown quantum states and use it to optimize our state-estimate feedback. Using Monte Carlo simulations, we study our protocol for the three-qubit bit-flip code in detail and demonstrate that it can improve the fidelity of quantum states beyond what is achievable using quantum error correction when the time between quantum error correction cycles is limited.Comment: 12 pages, 6 figures, REVTeX; references fixe

Decoherence control in microwave cavities

We present a scheme able to protect the quantum states of a cavity mode against the decohering effects of photon loss. The scheme preserves quantum states with a definite parity, and improves previous proposals for decoherence control in cavities. It is implemented by sending single atoms, one by one, through the cavity. The atomic state gets first correlated to the photon number parity. The wrong parity results in an atom in the upper state. The atom in this state is then used to inject a photon in the mode via adiabatic transfer, correcting the field parity. By solving numerically the exact master equation of the system, we show that the protection of simple quantum states could be experimentally demonstrated using presently available experimental apparatus.Comment: 13 pages, RevTeX, 8 figure

State and dynamical parameter estimation for open quantum systems

Following the evolution of an open quantum system requires full knowledge of its dynamics. In this paper we consider open quantum systems for which the Hamiltonian is ``uncertain''. In particular, we treat in detail a simple system similar to that considered by Mabuchi [Quant. Semiclass. Opt. 8, 1103 (1996)]: a radiatively damped atom driven by an unknown Rabi frequency $\Omega$ (as would occur for an atom at an unknown point in a standing light wave). By measuring the environment of the system, knowledge about the system state, and about the uncertain dynamical parameter, can be acquired. We find that these two sorts of knowledge acquisition (quantified by the posterior distribution for $\Omega$, and the conditional purity of the system, respectively) are quite distinct processes, which are not strongly correlated. Also, the quality and quantity of knowledge gain depend strongly on the type of monitoring scheme. We compare five different detection schemes (direct, adaptive, homodyne of the $x$ quadrature, homodyne of the $y$ quadrature, and heterodyne) using four different measures of the knowledge gain (Shannon information about $\Omega$, variance in $\Omega$, long-time system purity, and short-time system purity).Comment: 14 pages, 18 figure