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arXiv:1303.6830 · Physical Review A

Stochastic excitation during the decay of a two-level emitter subject to homodyne and heterodyne detection

Anders Bolund, Klaus Mølmer

Published Feb 18, 2014• 16 citations
arXivHTMLPDF

Abstract

We study the dynamics of an atomic two-level system decaying by spontaneous emission of light. Subject to continuous detection of the radiated field, the system tends with certainty to the ground state in the long time limit, but at initial times the excited-state population exhibits nontrivial stochastic behavior. Employing methods from Ito calculus, we characterize this behavior in case of unit efficiency detection, and we show, for example, that the emitter, as a result of in-phase homodyne measurements, may become fully excited during the decay process while heterodyne and out-of-phase homodyne measurements do not drive the atom completely into the excited state.

DOI
10.1103/physreva.89.023827

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We study the dynamics of an atomic two-level system decaying by spontaneous emission of light. Subject to continuous detection of the radiated field, the system tends with certainty to the ground state in the long time limit, but at initial times the excited-state population exhibits nontrivial stochastic behavior. Employing methods from Ito calculus, we characterize this behavior in case of unit efficiency detection, and we show, for example, that the emitter, as a result of in-phase homodyne measurements, may become fully excited during the decay process while heterodyne and out-of-phase homodyne measurements do not drive the atom completely into the excited state.
The evolution of a quantum state undergoing radiative decay depends on how its emission is detected. If the emission is detected in the form of energy quanta, the evolution is characterized by a quantum jump to a lower energy state. In contrast, detection of the wave nature of the emitted radiation leads to different dynamics. Here, we investigate the diffusive dynamics of a superconducting artificial atom under continuous homodyne detection of its spontaneous emission. Using quantum state tomography, we characterize the correlation between the detected homodyne signal and the emitter's state, and map out the conditional back-action of homodyne measurement. By tracking the diffusive quantum trajectories of the state as it decays, we characterize selective stochastic excitation induced by the choice of measurement basis. Our results demonstrate dramatic differences from the quantum jump evolution associated with photodetection and highlight how continuous field detection can be harnessed to control quantum evolution.
The Landau-Zener formula provides an analytical expression for the final excitation of a quantum system after passage of an avoided crossing of two energy levels. If the two levels correspond to a ground state and to an excited state which is subject to radiative decay, the probability of exciting the system by adiabatic passage of the level crossing is reduced. In this article we use a stochastic master equation to study the level crossing dynamics when the system is subject to continuous probing of the emitted radiation. The measurement back action on the system associated with the fluctuating homodyne detection record alters the level crossing dynamics, leading to significant excitation in spite of decay and imperfect transfer.
We have theoretically studied the effect of deterministic temporal control of spontaneous emission in a dynamic optical microcavity. We propose a new paradigm in light emission: we envision an ensemble of two-level emitters in an environment where the local density of optical states is modified on a time scale shorter than the decay time. A rate equation model is developed for the excited state population of two-level emitters in a time-dependent environment in the weak coupling regime in quantum electrodynamics. As a realistic experimental system, we consider emitters in a semiconductor microcavity that is switched by free-carrier excitation. We demonstrate that a short temporal increase of the radiative decay rate depletes the excited state and drastically increases the emission intensity during the switch time. The resulting time-dependent spontaneous emission shows a distribution of photon arrival times that strongly deviates from the usual exponential decay: A deterministic burst of photons is spontaneously emitted during the switch event.
A Schrödinger representation approach is used to calculate the atom-field dynamics following spontaneous emission by an atom in its excited state to a superposition of its two ground-state sublevels, in the case where the frequency separation of the ground-state sublevels is large compared to the excited-state decay rate. The emitted radiation is incident on a broadband photodetector. Using a relatively simple model for the photodetector, we show how a measurement of a photo-signal leaves the atom in a coherent superposition of the two ground states. The relative phase between the two ground-state amplitudes can be interpreted in terms of the temporal phase acquired in the time interval between spontaneous emission (viewed as a quantum jump process) and detection. Alternatively, the phase can be associated with a spatial phase of the entangled atom-field system; the source atom is projected into a state containing this spatial phase when the emitted photon is detected.
In this paper we investigate the dynamics of a model for a three-level atom in interaction with a radiation field. The exact solution to the spontaneous-emission problem is derived using methods developed earlier by the authors, and expressions are obtained for the probabilities of the atom’s being in the first or second excited states at any time t. For the special case that the strengths of the coupling between each of the excited states and the λth mode of the field are proportional, detailed conclusions can be drawn concerning the effects of such factors as system size, coupling function, and level splitting on the temporal evolution of the system. The evolution of excited quantum systems having one versus two modes of decay to the ground state is also compared, and similarities and differences in the temporal behavior are noted. Finally the relevance of the theory presented in this paper to experimental problems in radiation chemistry and physics is indicated in our concluding remarks.