arXiv subjects

Jürgen Audretsch

Publications and source records attributed to Jürgen Audretsch.

7 recordsLinked to original sources

arXiv2007

Parameter estimation for mixed states from a single copy

Given a single copy of a mixed state of the form ρ=λρ_1+(1-λ)ρ_2, what is the optimal measurement to estimate the parameter λ, if ρ_1 and ρ_2 are known? We present a general strategy to obtain the optimal measurements employing a Bayesian estimator. The measurements are chosen to minimize the deviation between the estimated- and the true value of λ. We explicitly determine the optimal measurements for a general two-dimensional system and for important higher dimensional cases.

quant-ph↗

arXiv2004

Monitoring Quantum Oscillations with very small Disturbance

We present a new scheme to detect and visualize oscillations of a single quantum system in real time. The scheme is based upon a sequence of very weak generalized measurements, distinguished by their low disturbance and low information gain. Accumulating the information from the single measurements by means of an appropriate Bayesian Estimator, the actual oscillations can be monitored nevertheless with high accuracy and low disturbance. For this purpose only the minimum and the maximum expected oscillation frequency need to be known. The accumulation of information is based on a general derivation of the optimal estimator of the expectation value of a hermitian observable for a sequence of measurements. At any time it takes into account all the preceding measurement results.

quant-ph↗

arXiv2002

Estimating the post-measurement state

We study generalized measurements (POVM measurements) on a single d-level quantum system which is in a completely unknown pure state, and derive the best estimate of the post-measurement state. The mean post-measuremement estimation fidelity of a generalized measurement is obtained and related to the operation fidelity of the device. This illustrates how the information gain about the post-measurement state and the corresponding state disturbance are mutually dependent. The connection between the best estimates of the pre- and post-measurement state is established and interpreted. For pure generalized measurements the two states coincide.

quant-ph↗

arXiv2001

Quantum optical weak measurements can visualize photon dynamics in real time

An experiment is proposed to visualize stroboscopically in real time the dynamics of a photon oscillating between two cavities. The visualization is implemented by a sequence of weak measurements (POVM), which are carried out by probing one of the cavities with a Rydberg atom and detecting a resulting phase shift by Ramsey interferometry. This way to measure the number of photons in a cavity was experimentally realized by Brune et al.. We suggest a feedback mechanism which minimizes the disturbance due to the measurement and enables a detection of the original evolution of the radiation field. PACS numbers: 03.65.Ta, 32.80.-t, 03.67.-a

quant-ph↗

arXiv1997

Continuous Fuzzy Measurement of Energy for a Two-Level System

A continuous measurement of energy which is sharp (perfect) leads to the quantum Zeno effect (freezing of the state). Only if the quantum measurement is fuzzy, continuous monitoring gives a readout E(t) from which information about the dynamical development of the state vector of the system may be obtained in certain cases. This is studied in detail. Fuzziness is thereby introduced with the help of restricted path integrals equivalent to non-Hermitian Hamiltonians. For an otherwise undisturbed multilevel system it is shown that this measurement represents a model of decoherence. If it lasts long enough, the measurement readout discriminates between the energy levels and the von Neumann state reduction is obtained. For a two-level system under resonance influence (which undergoes in absence of measurement Rabi oscillations between the levels) different regimes of measurement are specified depending on its duration and fuzziness: 1) the Zeno regime where the measurement results in a freezing of the transitions between the levels and 2) the Rabi regime when the transitions maintain. It is shown that in the Rabi regime at the border to the Zeno regime a correlation exists between the time dependent measurement readout and the modified Rabi oscillations of the state of the measured system. Possible realizations of continuous fuzzy measurements of energy are sketched.

quant-ph↗

arXiv1996

Actio causes reactio: Gravito-optical trapping of three-level atoms

We investigate an atomic three-level $Λ$-system which is exposed to two counterpropagating laser fields (inducing Raman transitions) and which is closed by a magnetic hyperfine field tuned to be in resonance with the transition between the two ground states. The influence of a homogeneous gravitational field is included in a full quantum treatment of the internal and external dynamics of the atom. It is shown that the combined influence of the gravitational field and the lasers lead for specific momentum values with a very high probability to a transition of the Landau-Zener type. This is accompanied by a momentum transfer resulting in an upward kick. For appropriate initial conditions a sequence of up and down motions is obtained. No mirror is needed. A gravito-optical trapping of atoms based on this effect seems to be realizable.

atom-ph↗

arXiv1994

Ramsey fringes in atomic interferometry: measurability of the influence of space-time curvature

The influence od space-time curvature on quantum matter which can be theoretically described by covariant wave equations has not been experimentally established yet. In this paper we analyse in detail the suitability of the Ramsey atom beam interferometer for the measurement of the phase shift caused by the Riemannian curvature of the earth. It appears that the detection should be possible with minor modifications of existing devices within the near future. The paper is divided into two parts. The first one is concerned with the derivation of general relativistic correction terms to the Pauli equation starting from the fully covariant Dirac equation and their physical interpretation. The inertial effects of acceleration and rotation are included. In the second part we calculate the phase shift as seen in a laboratory resting on the rotating earth and examine various possibilities to enlarge the sensitivity of the apparatus to space-time curvature. Some remarks on the Lense-Thirring effect and on gravitational waves are made. Since the two parts may be more or less interesting for physicists with different research fields they are written in such a way that each one may be read without much reference to the other one.

gr-qc↗