arXiv subjects

Kurt Jacobs

Publications and source records attributed to Kurt Jacobs.

At least 91 records · Page 5Linked to original sources

arXiv2011

Frequency Tracking and Parameter Estimation for Robust Quantum State-Estimation

In this paper we consider the problem of tracking the state of a quantum system via a continuous measurement. If the system Hamiltonian is known precisely, this merely requires integrating the appropriate stochastic master equation. However, even a small error in the assumed Hamiltonian can render this approach useless. The natural answer to this problem is to include the parameters of the Hamiltonian as part of the estimation problem, and the full Bayesian solution to this task provides a state-estimate that is robust against uncertainties. However, this approach requires considerable computational overhead. Here we consider a single qubit in which the Hamiltonian contains a single unknown parameter. We show that classical frequency estimation techniques greatly reduce the computational overhead associated with Bayesian estimation and provide accurate estimates for the qubit frequency

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arXiv2011

Entangled State Synthesis for Superconducting Resonators

We present a theoretical analysis of methods to synthesize entangled states of two superconducting resonators. These methods use experimentally demonstrated interactions of resonators with artificial atoms, and offer efficient routes to generate nonclassical states. We analyze physical implementations, energy level structure, and the effects of decoherence through detailed dynamical simulations.

quant-ph↗

arXiv2011

Arbitrary Control of Entanglement between Two Superconducting Resonators

We present a method to synthesize an arbitrary quantum state of two superconducting resonators. This state-synthesis algorithm utilizes a coherent interaction of each resonator with a tunable artificial atom to create entangled quantum superpositions of photon number (Fock) states in the resonators. We theoretically analyze this approach, showing that it can efficiently synthesize NOON states, with large photon numbers, using existing technology.

quant-ph↗

arXiv2011

Ultra-Efficient Cooling of Resonators: Beating Sideband Cooling with Quantum Control

The present state-of-the-art in cooling mechanical resonators is a version of "sideband" cooling. Here we present a method that uses the same configuration as sideband cooling --- coupling the resonator to be cooled to a second microwave (or optical) auxiliary resonator --- but will cool significantly colder. This is achieved by varying the strength of the coupling between the two resonators over a time on the order of the period of the mechanical resonator. As part of our analysis, we also obtain a method for fast, high-fidelity quantum information-transfer between resonators.

quant-ph↗

arXiv2011

Real-time feedback control of a mesoscopic superposition

We show that continuous real-time feedback can be used to track, control, and protect a mesoscopic superposition of two spatially separated wave-packets. The feedback protocol is enabled by an approximate state-estimator, and requires two continuous measurements, performed simultaneously. For nanomechanical and superconducting resonators, both measurements can be implemented by coupling the resonators to superconducting qubits.

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arXiv2010

Rapid purification of quantum systems by measuring in a feedback-controlled unbiased basis

Rapid-purification by feedback --- specifically, reducing the mean impurity faster than by measurement alone --- can be achieved by making the eigenbasis of the density matrix to be unbiased relative to the measurement basis. Here we further examine the protocol introduced by Combes and Jacobs [Phys.Rev.Lett. {\bf 96}, 010504 (2006)] involving continuous measurement of the observable $J_z$ for a $D$-dimensional system. We rigorously re-derive the lower bound $(2/3)(D+1)$ on the achievable speed-up factor, and also an upper bound, namely $D^2/2$, for all feedback protocols that use measurements in unbiased bases. Finally we extend our results to $n$ independent measurements on a register of $n$ qubits, and derive an upper bound on the achievable speed-up factor that scales linearly with $n$.

quant-ph↗

arXiv2010

Reflection of a Particle from a Quantum Measurement

We present a generalization of continuous position measurements that accounts for a spatially inhomogeneous measurement strength. This describes many real measurement scenarios, in which the rate at which information is extracted about position has itself a spatial profile, and includes measurements that detect if a particle has crossed from one region into another. We show that such measurements can be described, in their averaged behavior, as stochastically fluctuating potentials of vanishing time average. Reasonable constraints restrict the form of the measurement to have degenerate outcomes, which tend to drive the system to spatial superposition states. We present the results of quantum-trajectory simulations for measurements with a step-function profile (a "which-way" measurement) and a Gaussian profile. We find that the particle can coherently reflect from the measurement region in both cases, despite the stochastic nature of the measurement back-action. In addition, we explore the connection to the quantum Zeno effect, where we find that the reflection probability tends to unity as the measurement strength increases. Finally, we discuss two physical realizations of a spatially varying position measurement using atoms.

quant-ph↗

arXiv2010

Engineering Quantum States, Nonlinear Measurements, and Anomalous Diffusion by Imaging

We show that well-separated quantum superposition states, measurements of strongly nonlinear observables, and quantum dynamics driven by anomalous diffusion can all be achieved for single atoms or molecules by imaging spontaneous photons that they emit via resonance florescence. To generate anomalous diffusion we introduce continuous measurements driven by Lévy processes, and prove a number of results regarding their properties. In particular we present strong evidence that the only stable Lévy density that can realize a strictly continuous measurement is the Gaussian.

quant-ph↗

arXiv2010

Frequency Conversion: Side-band cooling, state-swapping, and coherent control of mechanical resonators

Sideband cooling is a technique that potentially allows mechanical resonators to be prepared in their ground states, important for future applications in quantum technologies. Tian has recently shown that side-band cooling can be implemented by modulating the coupling between a nano-resonator and a superconducting oscillator, a process of frequency conversion [L. Tian, PRB 79, 193407 (2009)]. While side-band cooling is usually treated in the steady-state regime, the effective resonant coupling will also generate near perfect state-swapping from the superconductor to the mechanical resonator. We perform numerical simulations of this system, examining the ground-state cooling achieved by the state-swapping. Further, we show that the superconducting oscillator can be used to control the amplitude and phase of the resonator, while simultaneously cooling it, and thus act as a coherent "quantum feedback controller".

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arXiv2010

A wave-function Monte Carlo method for simulating conditional master equations

Wave-function Monte Carlo methods are an important tool for simulating quantum systems, but the standard method cannot be used to simulate decoherence in continuously measured systems. Here we present a new Monte Carlo method for such systems. This was used to perform the simulations of a continuously measured nano-resonator in [Phys. Rev. Lett. 102, 057208 (2009)].

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arXiv2009

Engineering Giant Nonlinearities in Quantum Nanosystems

We describe a method to engineer giant nonlinearities in, and probes to measure nonlinear observables of, mesoscopic quantum resonators. This involves tailoring the Hamiltonian of a simple auxiliary system perturbatively coupled to the resonator, and has the potential to engineer a wide range of nonlinearities to high accuracy. We give a number of explicit examples, including a readily realizable two-qubit auxiliary system that creates an x^4 potential and a Chi^(3) (Kerr) nonlinearity, valid to fifth-order in the perturbative coupling.

quant-ph↗

arXiv2009

The Second Law of Thermodynamics and Quantum Feedback Control: Maxwell's Demon with Weak Measurements

Recently Sagawa and Ueda [Phys. Rev. Lett. 100, 080403 (2008)] derived a bound on the work that can be extracted from a quantum system with the use of feedback control. They left open the question of whether this bound could be achieved for every measurement that could be made by the controller. We show that it can, and that this follows straightforwardly from recent work on Maxwell's demon by Alicki et al. [Open Syst. Inform. Dynam. 11, 205 (2004)], for both discrete and continuous feedback control. Our analysis also shows that bare, efficient measurements always do non-negative work on a system in equilibrium, but do not add heat.

quant-ph↗

arXiv2009

Feedback Control Using Only Quantum Back-Action

The traditional approach to feedback control is to apply forces to a system by modifying the Hamiltonian. Here we show that quantum systems can be controlled without any Hamiltonian feedback, purely by exploiting the random quantum back-action of a continuous weak measurement. We demonstrate that, quite remarkably, the quantum back-action of such an adaptive measurement is just as effective at controlling quantum systems as traditional feedback.

quant-ph↗

arXiv2009

Comment on "Non-monotonicity in the Quantum-Classical Transition: Chaos Induced by Quantum Effects"

In a recent Letter [PRL 101, 074101 (2008)], Kapulkin and Pattanayak presented evidence that a quantum Duffing oscillator, sufficiently damped so that it is not classically chaotic, becomes chaotic in the transition region between quantum and classical motion. If true, this would be a striking result. However, Kapulkin and Pattanayak did not calculate the Lyapunov exponent for the system, usually regarded as the litmus-test of chaos. Here we perform this calculation, which throws considerable doubt upon their conclusions.

quant-ph↗

arXiv2009

Engineering Superposition States and Tailored Probes for Nano-resonators Via Open-Loop Control

We show that a nano-resonator can be prepared in mesoscopic-superposition states merely by monitoring a qubit coupled to the square of the resonators position. This works for thermal initial states, and does not require a third-order nonlinearity. The required coupling can be generated using a simple open-loop control protocol, obtained with optimal control theory. We simulate the complete preparation process, including environmental noise. Our results indicate the power of open-loop control for state-engineering and measurement in quantum nano-systems.

cond-mat.mes-hall↗

arXiv2009

The Equations of Quantum Feedback Control in the Regime of Good Control

We derive the equations of motion describing the feedback control of quantum systems in the regime of "good control", in which the control is sufficient to keep the system close to the desired state. One can view this regime as the quantum equivalent of the "linearized" regime for feedback control of classical nonlinear systems. Strikingly, while the dynamics of a single qubit in this regime is indeed linear, that of all larger systems remains nonlinear, in contrast to the classical case. As a first application of these equations, we determine the steady-state performance of feedback protocols for a single qubit that use unbiased measurements.

quant-ph↗

arXiv2009

A Monte Carlo Method for Modeling Thermal Damping: Beyond the Brownian-Motion Master Equation

The "standard" Brownian motion master equation, used to describe thermal damping, is not completely positive, and does not admit a Monte Carlo method, important in numerical simulations. To eliminate both these problems one must add a term that generates additional position diffusion. He we show that one can obtain a completely positive simple quantum Brownian motion, efficiently solvable, without any extra diffusion. This is achieved by using a stochastic Schroedinger equation (SSE), closely analogous to Langevin's equation, that has no equivalent Markovian master equation. Considering a specific example, we show that this SSE is sensitive to nonlinearities in situations in which the master equation is not, and may therefore be a better model of damping for nonlinear systems.

quant-ph↗

arXiv2008

Quantum Feedback Control: How to use Verification Theorems and Viscosity Solutions to Find Optimal Protocols

While feedback control has many applications in quantum systems, finding optimal control protocols for this task is generally challenging. So-called "verification theorems" and "viscosity solutions" provide two useful tools for this purpose: together they give a simple method to check whether any given protocol is optimal, and provide a numerical method for finding optimal protocols. While treatments of verification theorems usually use sophisticated mathematical language, this is not necessary. In this article we give a simple introduction to feedback control in quantum systems, and then describe verification theorems and viscosity solutions in simple language. We also illustrate their use with a concrete example of current interest.

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