We measure the quantum speed of the state evolution of the field in a weakly-driven optical cavity QED system. To this end, the mode of the electromagnetic field is considered as a quantum system of interest with a preferential coupling to a tunable environment: the atoms. By controlling the environment, i.e., changing the number of atoms coupled to the optical cavity mode, an environment assisted speed-up is realized: the quantum speed of the state re-population in the optical cavity increases with the coupling strength between the optical cavity mode and this non-Markovian environment (the number of atoms). PACS numbers: 42.50.Pq, 42.50.Lc,32.50.+d Identifying time-optimized processes is a ubiquitous goal in virtually all areas of quantum physics, such as quantum communication [1], quantum computation [2], quantum thermodynamics [3], quantum control and feedback [4], and quantum metrology [5]. To this end, the notion of a quantum speed limit (QSL) has proven to be useful and important. The QSL determines the theoretical upper bound on the speed of evolution of a quantum system. It can be understood as a generalization of the Heisenberg uncertainty relation for energy and time. It has been derived for isolated, uncontrolled systems [6-8], time-dependent Hamiltonians [9-13], and more recently for more general open system dynamics [14][15][16][17][18][19][20][21]. Although fundamental in nature, practical consequences or even experimental applications of the QSL are still lacking. Nevertheless, achieving the maximal quantum speed is of high practical relevance, especially in the development of quantum information processing devices.On the theoretical side, a recent study [14] hinted at the possibility of observing speed-ups of the quantum evolution if an open quantum system is subject to environmental changes. Ref. [14] analyzes the dynamics of the damped Jaynes-Cummings model, which describes many cavity QED systems. These systems in both the intermediate and strong coupling regime can exhibit environmentassisted evolution [22] -such as non-exponential decay.This letter reports an experimental realization of the theoretically proposed environment assisted speed-up [14]. To this end, we look at the system in an unusual way -as just consisting of the cavity field. This allows us to treat the atomic number that generates the atomic polarization (the off diagonal elements of the atomic master equation) as a tunable environment with a range of coupling constants. We demonstrate that increasing the interaction of the optical cavity field with the environment by tuning the number of atoms, modifies the time dependent non-classical intensity correlation function, enhancing -speeds-up-the rate of evolution of the cavity field in a range with no clear oscillations present.Our cavity QED system operates in the intermediate coupling regime, where the cavity-atom parameters are of the same order: (g, κ, γ) /2π = (3.2, 4.5, 6.0) MHz. Here g denotes the electric dipole interaction strength of an atom maximally coupled to th...
The spontaneous creation and persistence of ground-state coherence in an ensemble of intracavity Rb atoms has been observed as a quantum beat. Our system realizes a quantum eraser, where the detection of a first photon prepares a superposition of ground-state Zeeman sublevels, while detection of a second erases the stored information. Beats appear in the time-delayed photon-photon coincidence rate (intensity correlation function). We study the beats theoretically and experimentally as a function of system parameters, and find them remarkably robust against perturbations such as spontaneous emission. Although beats arise most simply through single-atom-mediated quantum interference, scattering pathways involving pairs of atoms interfere also in our intracavity experiment. We present a detailed model which identifies all sources of interference and accounts for experimental realities such as imperfect pre-pumping of the atomic beam, cavity birefringence, and the transit of atoms across the cavity mode.
An anomalous light shift in the precession of a ground-state Zeeman coherence is observed: the Larmor frequency increases with the strength of a drive that is blue (red) detuned from a transition out of the lower (upper) energy level. Our measurements are made on 85 Rb atoms traversing an optical cavity containing a few photons; shifts as large as 1% per photon are recorded. The anomalous shift arises from an accumulation of phase driven by quantum jumps. It is stochastic and accompanied by broadening.Elastic Rayleigh scattering [1] is a ubiquitous process in the manipulation of atoms by light, and a widely used tool for the projective measurement of their quantum states. While its basic properties have long been known, subtleties continue to be uncovered. Uys et al. [2] have recently shown that its contribution to the decoherence rate of a ground-state superposition (two-level system) is given by the square of the difference of the scattering amplitudes; if the amplitudes interfere constructively, there is decoherence even when the rates of scattering from the two levels of the superposition are equal, contrasting previous work [3] that found such effects negligible.The elastic Rayleigh scattering considered by Uys et al. is exemplified by measurements on a 9 Be + ion, with a ground-to-excited-state detuning of tens of GHz, far in excess of the excited state linewidth. In this Letter, we report on an anomalous light shift observed in a quasiresonant system of 85 Rb atoms. This shift, which reverses the sign of the usual AC Stark shift, is similarly due to elastic Rayleigh scattering and driven by precisely the same mechanism as the decoherence reported in [2]. Most generally, decoherence and shift exist side by side, with the decoherence dominant far from resonance and the anomalous light shift dominant in the quasi-resonant regime. The two sides are unified by an analysis of the quantum-jump-driven evolution of coherence under elastic Rayleigh scattering.Our experimental observation is made through conditional detection of photons scattered from 85 Rb atoms into an optical cavity mode at moderate-to-weak dipole coupling strengths [4]. Detection of a first photon creates coherence between Zeeman-shifted ground states, |g − and |g + , where the Zeeman splitting is significantly smaller than the excited state linewidth and the cavity width. Evolution of this coherence is observed as a quantum beat written on the probability of a subsequent sec- * lorozco@umd.edu ond photon detection [5]. The beat note then reveals the anomalous shift: the observed Larmor frequency increases with the strength of a drive that is blue (red) detuned from the optical transition out of the lower (higher) ground state, opposite to what one would naively predict from the AC Stark effect applied to each ground-state level. We first explain the origin of this anomalous shift and its connection to the decoherence reported in [2] using a simplified model. We then present our experimental measurements, which we compare with full quantum traje...
Abstract. We implement a simple feedback mechanism on a two-mode cavity QED system to preserve the Zeeman coherence of a ground state superposition that generates quantum beats on the second-order correlation function. Our investigation includes theoretical and experimental studies that show how to prevent a shift away from the Larmor frequency and associated decoherence caused by Rayleigh scattering. The protocol consists of turning off the drive of the system after the detection of a first photon and letting it evolve in the dark. Turning the drive back on after a pre-set time reveals a phase accumulated only from Larmor precession, with the amplitude of the quantum beat more than a factor of two larger than with continuous drive.
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