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Physical Review A

Macroscopic quantum jumps from a two-atom system

Kazunari Yamada, P. R. Berman

Published Jan 1, 1990• 9 citations
Publisher

Abstract

We analyze the macroscopic quantum jumps (sudden interruptions in the fluorescence on a macroscopic time scale) that are produced when a pair of two-level atoms separated by a distance d is irradiated by a strong laser having wavelength ${\ensuremath{\lambda}}_{0}$, with ${\ensuremath{\lambda}}_{0}$\ensuremath{\gg}d. Included in the analysis is the dipole-dipole coupling of the atoms, the ac Stark effect, and the role played by a term that is present in the atom-laser field interaction Hamiltonian when k\ensuremath{\cdot}d\ensuremath{\ne}0 (k is the wave vector of the laser field and d is the vector connecting the two atoms). Our treatment is based on frequency-resolved delay functions, an extension of a concept developed by Reynaud, Dalibard, and Cohen-Tannoudji [IEEE J. Quantum Electron. 24, 1395 (1988)], which is shown to be useful to study frequency-resolved photon statistics. As examples, we study the statistics of the fluorescence produced by the two-atom system as well as those in the components of the fluorescent triplet produced by a single two-level atom.

DOI
10.1103/physreva.41.453

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We analyze the macroscopic quantum jumps (sudden interruptions in the fluorescence on a macroscopic time scale) that are produced when a pair of two-level atoms separated by a distance d is irradiated by a strong laser having wavelength \ensuremathλ0{\ensuremath{\lambda}}_{0}\ensuremathλ0​, with \ensuremathλ0{\ensuremath{\lambda}}_{0}\ensuremathλ0​\ensuremath{\gg}d. Included in the analysis is the dipole-dipole coupling of the atoms, the ac Stark effect, and the role played by a term that is present in the atom-laser field interaction Hamiltonian when k\ensuremath{\cdot}d\ensuremath{\ne}0 (k is the wave vector of the laser field and d is the vector connecting the two atoms). Our treatment is based on frequency-resolved delay functions, an extension of a concept developed by Reynaud, Dalibard, and Cohen-Tannoudji [IEEE J. Quantum Electron. 24, 1395 (1988)], which is shown to be useful to study frequency-resolved photon statistics. As examples, we study the statistics of the fluorescence produced by the two-atom system as well as those in the components of the fluorescent triplet produced by a single two-level atom.
We study analytically the effect of the dipole-dipole interaction on the statistics of the fluorescent radiation emitted from a system of two two-level atoms resonantly driven by a coherent field. For some interatomic separations, an inhibition of fluorescence occurs, which is reminiscent of the recently discussed quantum-jump phenomenon in a single three-level atom. This is reflected in the behaviors of the intensity correlation function, Mandel's Q parameter, and the time-dependent fluorescence spectrum. It is argued that this quantum-jump-like behavior arises from the coupling between the symmetric states and the antisymmetric state caused by the dipole-dipole interaction.
We first use the quantum method to replicate the well-known results of a single atom relaxing, whilst demonstrating the intuitive picture it provides for dissipative dynamics. By use of individual "quantum trajectories", the method allows for simulation of systems inaccessible to ensemble treatments. This is shown by replicating resonance fluorescence, allowing us to concurrently demonstrate the method's facilitation of calculating photon statistics by the creation of discrete photon streams. To analyse these, we solidify the theoretical basis for, and implement, a computational method of calculating second-order coherence functions. A process by which to model interacting two-atom systems to allow for computation with the quantum jump method is then developed. Using this, we demonstrate cooperative effects leading to greatly modified emission spectra, before investigating the decoupling of states from dissipative and coherent interactions. Here, we find the novel insight provided by the quantum jump method both births and provides the tools with which to begin an investigation into the occurrence of macroscopic jumps and the formation of macroscopic dark periods in a system of two two-level dipole-dipole coupled atoms.
The statistics of spontaneous photon emission times in single atom resonance fluorescence are investigated through the radiative cascade of the dressed atom. The delay function which gives the distribution of the delays between two successive emissions is calculated for a coherent as well as an incoherent laser excitation. For a two-level atom, various signals that reflect the fluorescence intensity (average value, photon counting, fluctuation spectrum, etc.) are reviewed by this method. For a three-level atom, this approach is applied to the analysis of the recently observed phenomenon of intermittent fluorescence and quantum jumps.>
Phase-sensitive squeezing in the resonance fluorescence of two-level atoms, that are coherently driven by a near-resonant laser field in free space, was observed recently (Lu et al 1998 Phys. Rev .L ett. 81 3635). This was accomplished via homodyne detection at a phase near ±45 ◦ relative to the driving field for strong off-resonant excitation of ‘long-lived’ atoms (where th ea tomic lifetime far exceeded the laser–atom interaction time, meaning that relaxation effects could be ignored). On the other hand, traditional theoretical predictions of phase-sensitive squeezing in the resonance fluorescence from two-level atoms have emphasized in- and out-of-phase (i.e., 0 ◦ and 90 ◦ ) quadratures, and weak, on-resonant excitation of ‘short-lived’ atoms (where the observation time for laser–atom interaction fa re xceeded the natural atomic lifetime, meaning that relaxation effects dominate). Here, we calculate the probability of a delayed-coincidence detection in the interference field of a fluorescing dipole with a local oscillator (LO). We show that, despite the strikingly different conditions in which squeezing occurs in short- and long-lived atoms, squeezing in both cases can be shown to arise from a joint detection of two photons which are related by a quantum jump in the following way: the first photodetection precipitates a quantum jump of the atom to the ground state, and the second measures the mean amplitude of the fluorescent field subsequent to the quantum jump.
Attention is focused on the dynamic evolution of the emission spectrum following abrupt excitation of a near-resonant two-level absorber by a strong laser field. The multiphoton character of the absorption-emission process is evident in the AC Stark splitting of the spectrum, which begins approximately half an atomic lifetime after excitation, if the laser field is strong enough. Analytic expressions for the spectra are given of arbitrary laser field strength, atomic lifetime, laser-atom detuning, and the bandwidth of the spectrometer used to analyse the spectrum. Selected graphs are included to illustrate various time-dependent features of the spectrum. The influence on the transient spectrum of three different states of atomic excitation prior to laser irradiation and the effect on the spectrum of irradiation by a phase-noisy laser are also considered. Comparison of the transient spectra from atoms initially prepared in ' pi /2' and '3 pi /2' states show clearly that phase relationships between the irradiating field and the emitting dipole are important even in fluorescence.
The quantum jump statistics in the fluorescence intensity from two three-level atoms is studied. A rate-equation description valid for strong driving fields is derived, and a partial analysis of quantum jump statistics which goes beyond the strong-excitation limit is presented. As the main result, it is shown that collective effects, such as unusual intensity levels and double quantum jumps, can occur in two-atom systems. However, their observation requires that the atoms be localized within a wavelength of light.>