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arXiv:cond-mat/0606430 · Physical Review Letters

Continuous and Pulsed Quantum Zeno Effect

Erik W. Streed, Jongchul Mun, Micah Boyd, Gretchen K. Campbell, Patrick Medley, Wolfgang Ketterle, David E. Pritchard

Published Dec 27, 2006• 179 citations
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Abstract

Continuous and pulsed quantum Zeno effects were observed using a 87Rb Bose-Einstein condensate. Oscillations between two ground hyperfine states of a magnetically trapped condensate, externally driven at a transition rate omega(R), were suppressed by destructively measuring the population in one of the states with resonant light. The suppression of the transition rate in the two-level system was quantified for pulsed measurements with a time interval deltat between pulses and continuous measurements with a scattering rate gamma. We observe that the continuous measurements exhibit the same suppression in the transition rate as the pulsed measurements when gammadeltat=3.60(0.43), in agreement with the predicted value of 4. Increasing the measurement rate suppressed the transition rate down to 0.005 omega(R).

DOI
10.1103/physrevlett.97.260402

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Continuous and pulsed quantum Zeno effects were observed using a 87Rb Bose-Einstein condensate. Oscillations between two ground hyperfine states of a magnetically trapped condensate, externally driven at a transition rate omega(R), were suppressed by destructively measuring the population in one of the states with resonant light. The suppression of the transition rate in the two-level system was quantified for pulsed measurements with a time interval deltat between pulses and continuous measurements with a scattering rate gamma. We observe that the continuous measurements exhibit the same suppression in the transition rate as the pulsed measurements when gammadeltat=3.60(0.43), in agreement with the predicted value of 4. Increasing the measurement rate suppressed the transition rate down to 0.005 omega(R).
The quantum Zero effect is the inhibition of transitions between quantum states by frequent measurements of the state. The inhibition arises because the measurement causes a collapse (reduction) of the wave function. If the time between measurements is short enough, the wave function usually collapses back to the initial state. We have observed this effect in an rf transition between two 9^{9}9Be+{\mathrm{Be}}^{+}Be+ ground-state hyperfine levels. The ions were confined in a Penning trap and laser cooled. Short pulses of light, applied at the same time as the rf field, made the measurements. If an ion was in one state, it scattered a few photons; if it was in the other, it scattered no photons. In the latter case the wave-function collapse was due to a null measurement. Good agreement was found with calculations.
Abstract We present a numerical study of measurement-induced suppression of coherent tunneling in a two-level quantum system subject to re peated projective monitoring. The dynamics are simulated using a stochastic quantum-trajectory (Monte-Carlo) unraveling which repro duces the dephasing dynamics of a continuously monitored system. We introduce an effective measurement rate γ ≈ pmeas/dt and demon strate a monotonic reduction of the escaped population as a function of γ/∆, where ∆ is the coherent tunneling amplitude. For a fixed evolution time T = π/2, we observe a clear transition to the quantum Zeno regime for γ ≫ ∆. A log–log analysis of the large-γ data re veals an asymptotic scaling close to Pesc ∝ γ−1, in agreement with the strong-measurement limit of the corresponding Lindblad master equation. Our results provide a compact and programmable numerical platform for investigating measurement-controlled tunneling dynamics and Zeno-based control using gate-level quantum simulation frame works.
We propose an experiment to observe the quantum Zeno effect in atomic Bragg scattering. The quantum Zeno effect is the inhibition of the free evolution of a system when that system is subject to a decohering measurement process. This effect is usually studied theoretically in an idealized two-level system, though this system has been difficult to realize in practice. The coherent population exchange between the forward and Bragg beams provides an ideal two-level system, though as there is no practical scheme for continuously monitoring the motion of an atom we include decoherence by adding noise to the laser. Using the method of stochastic Hamiltonians we show that the noise suppresses tunneling in the two-state system and, in the large noise limit, the system can freeze in its initial state.
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
Laser-cooled ions stored in Penning traps are essentially free from collisions and other perturbations that could cause relaxations. This, and the fact that their energy levels can easily be manipulated with rf and laser radiation, makes them well suited for demonstrating certain aspects of quantum measurement theory. The quantum Zeno effect is the inhibition of transitions between states by frequent measurements.1 We have observed this effect in a 9Be+ ground-state rf transition. The measurements are short pulses of light. If the ion is in one state, it scatters a few photons; if it is in the other, it scatters no photons. In the latter case the wavefunction collapse is due to a null measurement.2 The dynamics of this system are similar to those which are predicted to lead to nonexponential spontaneous decay at short times.