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Gerhard C. Hegerfeldt

Publications and source records attributed to Gerhard C. Hegerfeldt.

32 records · Page 2Linked to original sources
arXiv1999

Cooperative effects in the light and dark periods of two dipole-interacting atoms

If an atom is able to exhibit macroscopic dark periods, or electron shelving, then a driven system of two atoms has three types of fluorescence periods (dark, single and double intensity). We propose to use the average durations of these fluorescence types as a simple and easily accessible indicator of cooperative effects. As an example we study two dipole-interacting V systems by simulation techniques. We show that the durations of the two types of light periods exhibit marked separation-dependent oscillations and that they vary in phase with the real part of the dipole-dipole coupling constant.

quant-ph↗
arXiv1998

Instantaneous Spreading and Einstein Causality in Quantum Theory

In nonrelativistic quantum mechanics the wave-function of a free particle which initially is in a finite volume immediately spreads to infinity. In a nonrelativistic theory this is of no concern, but we show that the same instantaneous spreading can occur in relativistic quantum theory and that transition probabilities in widely separated systems may instantaneously become nonzero. We discuss how this affects Einstein causality.

quant-ph↗
arXiv1998

Transition from antibunching to bunching for two dipole-interacting atoms

It is known that there is a transition from photon antibunching to bunching in the resonance fluorescence of a driven system of two two-level atoms with dipole-dipole interaction when the atomic distance decreases and the other parameters are kept fixed. We give a simple explanation for the underlying mechanism which in principle can also be applied to other systems. PACS numbers 42.50.Ar, 42.50Fx

quant-ph↗
arXiv1997

Ensemble versus individual system in quantum optics

Modern techniques allow experiments on a single atom or system, with new phenomena and new challenges for the theoretician. We discuss what quantum mechanics has to say about a single system. The quantum jump approach as well as the role of quantum trajectories are outlined and a rather sophisticated example is given.

quant-ph↗
arXiv1997

Atomic versus molecular diffraction: Influence of break-ups and finite size

Atomic diffraction through double slits and transmission gratings is well described in terms of the associated de Broglie waves and classical wave optics. However, for weakly bound and relatively large systems, such as the He_2 dimer, this might no longer hold true due to the possibility of break-up processes and finite-size effects. We therefore study the diffraction of weakly bound two-particle systems. If the bar and slit widths of the grating are much larger than the diameter of the two-particle system we recover the usual optics results. For smaller widths, however, deviations therefrom occur. We find that the location of possible diffraction peaks is indeed still governed by the usual grating function from optics, but the peaks may have a lower intensity. This is not unexpected when break-up processes are allowed. More unusually though, diffraction peaks which would be absent for de Broglie waves may reappear. The results are illustrated for diffraction of He_2.

quant-ph↗
arXiv1997

Problems about Causality in Fermi's Two-Atom Model and Possible Resolutions

In order to check finite propagation speed Fermi, in 1932, had considered two atoms A and B separated by some distance R. At time t=0, A is in an excited state, B in its ground state, and no photons are present. Fermi's idea was to calculate the excitation probability of B. In a model-independent way and with minimal assumptions - Hilbert space and positive energy only - it is proved, not just for atoms but for any systems A and B, that the excitation probability of B is nonzero immediately after t=0. Possible ways out to avoid a contradiction to finite propagation speed are discussed. The notions of strong and weak Einstein causality are introduced.

quant-ph↗
arXiv1996

Quantum Zeno Effect and Light-Dark Periods for a Single Atom

The quantum Zeno effect (QZE) predicts a slow-down of the time development of a system under rapidly repeated ideal measurements, and experimentally this was tested for an ensemble of atoms using short laser pulses for non-selective state measurements. Here we consider such pulses for selective measurements on a single system. Each probe pulse will cause a burst of fluorescence or no fluorescence. If the probe pulses were strictly ideal measurements, the QZE would predict periods of fluorescence bursts alternating with periods of no fluorescence (light and dark periods) which would become longer and longer with increasing frequency of the measurements. The non-ideal character of the measurements is taken into account by incorporating the laser pulses in the interaction, and this is used to determine the corrections to the ideal case. In the limit, when the time between the laser pulses goes to zero, no freezing occurs but instead we show convergence to the familiar macroscopic light and dark periods of the continuously driven Dehmelt system. An experiment of this type should be feasible for a single atom or ion in a trap

quant-ph↗
arXiv1996

Atomic Quantum Zeno Effect for Ensembles and Single Systems

The so-called quantum Zeno effect is essentially a consequence of the projection postulate for ideal measurements. To test the effect Itano et al. have performed an experiment on an ensemble of atoms where rapidly repeated level measurements were realized by means of short laser pulses. Using dynamical considerations we give an explanation why the projection postulate can be applied in good approximation to such measurements. Corrections to ideal measurements are determined explicitly. This is used to discuss in how far the experiment of Itano et al. can be considered as a test of the quantum Zeno effect. We also analyze a new possible experiment on a single atom where stochastic light and dark periods can be interpreted as manifestation of the quantum Zeno effect. We show that the measurement point of view gives a quick and intuitive understanding of experiments of the above type, although a finer analysis has to take the corrections into account.

quant-ph↗
arXiv1996

State Measurements with Short Laser Pulses and Lower-Efficiency Photon Detectors

It has been proposed by Cook (Phys. Scr. T 21, 49 (1988)) to use a short probe laser pulse for state measurements of two-level systems. In previous work we have investigated to what extent this proposal fulfills the projection postulate if ideal photon detectors are considered. For detectors with overall efficiency less than 1 complications arise for single systems, and for this case we present a simple criterion for a laser pulse to act as a state measurement and to cause an almost complete state reduction.

atom-ph↗
arXiv1996

Laser Pulses as Measurements. Application to the Quantum Zeno Effect

Short pulses of a probe laser have been used in the past to measure whether a two-level atom is in its ground or excited state. The probe pulse couples the ground state to a third, auxiliary, level of the atom. Occurrence or absence of resonance fluorescence were taken to mean that the atom was found in its ground or excited state, respectively. In this paper we investigate to what extent this procedure results in an effective measurement to which the projection postulate can be applied, at least approximately. We discuss in detail the complications arising from an additional time development of the two-level system proper during a probe pulse. We extend our previous results for weak probe pulses to the general case and show that one can model an ideal (projection-postulate) measurement much better with a strong than a weak probe pulse. In an application to the quantum Zeno effect we calculate the slow-down of the atomic time development under n repeated probe pulse measurements and determine the corrections compared to the case of n ideal measurements.

quant-ph↗
arXiv1995

Conditional Hamiltonian and Reset Operator in the Quantum Jump Approach

For the time development of a single system in the quantum jump approach or for quantum trajectories one requires the conditional (reduced) Hamiltonian between jumps and the reset operator after a jump. Explicit expressions for them are derived for a general N-level system by employing the same assumptions as in the usual derivation of the Bloch equations. We discuss a possible minor problem with positivity for these expressions as well as for the corresponding Bloch equations.

atom-ph↗
arXiv1995

Projection Postulate and Atomic Quantum Zeno Effect

The projection postulate has been used to predict a slow-down of the time evolution of the state of a system under rapidly repeated measurements, and ultimately a freezing of the state. To test this so-called quantum Zeno effect an experiment was performed by Itano et al. (Phys. Rev. A 41, 2295 (1990)) in which an atomic-level measurement was realized by means of a short laser pulse. The relevance of the results has given rise to controversies in the literature. In particular the projection postulate and its applicability in this experiment have been cast into doubt. In this paper we show analytically that for a wide range of parameters such a short laser pulse acts as an effective level measurement to which the usual projection postulate applies with high accuracy. The corrections to the ideal reductions and their accumulation over n pulses are calculated. Our conclusion is that the projection postulate is an excellent pragmatic tool for a quick and simple understanding of the slow-down of time evolution in experiments of this type. However, corrections have to be included, and an actual freezing does not seem possible because of the finite duration of measurements.

quant-ph↗