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arXiv:1601.00451 · New Journal of Physics

Interplay of classical and quantum dynamics in a thermal ensemble of atoms

Arif Warsi Laskar, Niharika Singh, Arunabh Mukherjee, Saikat Ghosh

Published May 12, 2016• 8 citations

Abstract

In a thermal ensemble of atoms driven by coherent fields, how does evolution of quantum superposition compete with classical dynamics of optical pumping and atomic diffusion? Is it optical pumping that first prepares a thermal ensemble, with coherent superposition developing subsequently or is it the other way round: coherently superposed atoms driven to steady state via optical pumping? Using a stroboscopic probing technique, here we experimentally explore these questions. A 100 ns pulse is used to probe an experimentally simulated, closed three-level, Λ-like configuration in rubidium atoms, driven by strong coherent ( control ) and incoherent fields. Temporal evolution of probe transmission shows an initial overshoot with turn-on of control , resulting in a scenario akin to lasing without inversion. The corresponding rise time is dictated by coherent dynamics, with a distinct experimental signature of half-cycle Rabi flop in a thermal ensemble of atoms. Our results indicate that, in fact, optical pumping drives the atoms to a steady state in a significantly longer time-scale that sustains superposed dark states . Eventual control turn-off leads to a sudden fall in transmission with an ubiquitous signature for identifying closed and open systems. Numerical simulations and toy-model predictions confirm our claims. These studies reveal new insights into a rich and complex dynamics associated with atoms in thermal ensemble, which are otherwise absent in state-prepared, cold atomic ensembles.

DOI: 10.1088/1367-2630/18/5/053022

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In a thermal ensemble of atoms driven by coherent fields, how does evolution of quantum superposition compete with classical dynamics of optical pumping and atomic diffusion? Is it optical pumping that first prepares a thermal ensemble, with coherent superposition developing subsequently or is it the other way round: coherently superposed atoms driven to steady state via optical pumping? Using a stroboscopic probing technique, here we experimentally explore these questions. A 100 ns pulse is used to probe an experimentally simulated, closed three-level, Λ-like configuration in rubidium atoms, driven by strong coherent ( control ) and incoherent fields. Temporal evolution of probe transmission shows an initial overshoot with turn-on of control , resulting in a scenario akin to lasing without inversion. The corresponding rise time is dictated by coherent dynamics, with a distinct experimental signature of half-cycle Rabi flop in a thermal ensemble of atoms. Our results indicate that, in fact, optical pumping drives the atoms to a steady state in a significantly longer time-scale that sustains superposed dark states . Eventual control turn-off leads to a sudden fall in transmission with an ubiquitous signature for identifying closed and open systems. Numerical simulations and toy-model predictions confirm our claims. These studies reveal new insights into a rich and complex dynamics associated with atoms in thermal ensemble, which are otherwise absent in state-prepared, cold atomic ensembles.

Coherent dark states in atoms, created by simultaneous interaction of two coherent light fields with a 3-level system, are of prime importance in quantum state manipulation. They are used extensively in quantum sensing and quantum information applications to build atomic clocks, magnetometers, atomic interferometers and more. Here we study the formation and decay of coherent dark-states in an ensemble of laser-cooled free-falling atoms. We measure the optical-pumping rate into the dark-state in the

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polarization configuration. We find that the pumping rate is linear with the optical field intensity, but about an order-of-magnitude slower than the rate predicted by the commonly used, but simplistic, three-level analytic formula. Using a numerical model we demonstrate that this discrepancy is due to the multi-level Zeeman manifold. Taking into account the slower pumping rate we explain quantitatively the relation between the light-shift and the duration of pumping into dark-state in Ramsey spectroscopy. We also measure the decay of the dark-state coherence and find that in our apparatus it is dominated by the mechanical motion of the atoms out of the probing region, while the atomic decoherence is negligible.

We present a theoretical study of quantum coherent dynamics of a three-level Λ-system driven by a thermal environment (such as blackbody radiation), which serves as an essential building block of photosynthetic light-harvesting models and quantum heat engines. By solving nonsecular Bloch–Redfield master equations, we obtain analytical results for the ground-state population and coherence dynamics and classify the dynamical regimes of the incoherently driven Λ-system as underdamped and overdamped depending on whether the ratio Δ/[rf(p)] is greater or less than one, where Δ is the ground-state energy splitting, r is the incoherent pumping rate, and f(p) is a function of the transition dipole alignment parameter p. In the underdamped regime, we observe long-lived coherent dynamics that lasts for τc ≃ 1/r, even though the initial state of the Λ-system contains no coherences in the energy basis. In the overdamped regime for p = 1, we observe the emergence of coherent quasi-steady states with the lifetime τc = 1.34(r/Δ2), which have a low von Neumann entropy compared to conventional thermal states. We propose an experimental scenario for observing noise-induced coherent dynamics in metastable He* atoms driven by x-polarized incoherent light. Our results suggest that thermal excitations can generate experimentally observable long-lived quantum coherent dynamics in the ground-state subspace of atomic and molecular Λ-systems in the absence of coherent driving.

In a micromaser where a classical field strongly drives the atoms while they cross the cavity, remarkable atom–atom correlations show up at steady state, which vanish much faster than dissipative decay. Hence we consider atom pair correlation measurements in which the detection of the first probe atom prepares a mesoscopic superposition state of the cavity field, that entangles with a second probe atom. The conditional probabilities for the latter atomic detection provide a description of the decoherence of the superposition state, occurring in an open system in the presence of pumping, driving, dissipative, and thermal effects. The decoherence rate scales as the squared interaction time, that sets the separation in phase space between the superposition components, whereas the quantum coherence is unaffected by the atomic pumping. Hence we further investigate the system when the cavity is not pumped. Starting the correlation measurements from a thermal state, we can describe the effect of temperature on decoherence. Starting from a vacuum state, the superposition states are maximally separated Schrodinger cat states, whose decoherence can thus be monitored.

We show that continuous-wave, two colour excitation of three-level atoms opens new channels of irreversible population transfer between atomic levels. This process, which we describe as dynamically induced irreversibility, leads to unanticipated phenomena including the inversion of atomic transitions whose upper atomic level has no conventional source of irreversible population pumping. We also study the effect of excitation-field bandwidth on the gain exhibited by driven, three-level, V-type atomic systems. Gain, which may or may not be inversionless in the atomic-state basis, is produced through strong monochromatic driving of one atomic transition and weaker pumping of a coupled transition. It is found that monochromatic pumping frequently yields greater optical gain than incoherent (wide bandwidth) pumping. This is particularly true when system gain can be attributed to hidden inversions among the eigenstates (semi-classical dressed states) of the coupled atom+driving field quantum system. Last, we report the observation of continuous-wave lasing in a strongly driven barium cascade system and interpret its properties in terms of the models presented.

We propose a state-dependent diffusion model for strongly driven thermal-atom spectra. Starting from the trajectory-dependent internal-state evolution of individual atoms, we derive a closed spatial equation for the local density-matrix field using a velocity-moment expansion. Measurements of an

^{85}

Rb atomic-filter transmission spectrum agree well with the model up to a maximum Gaussian peak intensity of

1.27\times10^{3}

W/cm

^2

, approaching six orders of magnitude above the

^{85}

Rb D2-line saturation intensity. Counterintuitively, the model reveals an anomalous optical-pumping pathway in which intense light transfers atoms from nominally dark states into bright states. Hyperfine Paschen--Back splitting selectively enhances this anomalous pathway while suppressing conventional optical pumping, allowing the filter to maintain approximately 97

\%

transmission at the highest intensity studied. This work provides a framework for controlling strongly driven atomic ensembles and designing saturation-resistant atomic optical devices.