Decoherence due to Elastic Rayleigh Scattering

Abstract

We present theoretical and experimental studies of the decoherence of hyperfine ground-state superpositions due to elastic Rayleigh scattering of light off-resonant with higher lying excited states. We demonstrate that under appropriate conditions, elastic Rayleigh scattering can be the dominant source of decoherence, contrary to previous discussions in the literature. We show that the elastic-scattering decoherence rate of a two-level system is given by the square of the difference between the elastic-scattering amplitudes for the two levels, and that for certain detunings of the light, the amplitudes can interfere constructively even when the elastic scattering rates from the two levels are equal. We confirm this prediction through calculations and measurements of the total decoherence rate for a superposition of the valence electron spin levels in the ground state of 9 Be + in a 4.5 T magnetic field.Off-resonant light scattering (spontaneous emission) is an important source of decoherence in many coherentcontrol experiments with atoms and molecules. Examples include the use of optical-dipole forces for gates in quantum computing [1], the generation of spin squeezed states through laser-mediated interactions [2][3][4][5][6], and the trapping and manipulation of neutral atoms in optical lattices [7,8]. These experiments frequently involve superpositions of two-level atomic systems (qubits) and use laser beams off-resonant with higher lying excited states to control and measure the atomic states.In general, decoherence of an atomic superposition state due to off-resonant light scattering occurs if the scattered photon carries information about the qubit state. During Raman scattering the initial and final qubit states differ. The state of the scattered photon is entangled with the atomic state, providing "welcherweg" (which-way) information and leading to decoherence [9,10]. By contrast the role of elastic Rayleigh scattering for decoherence is not as clear. Two very different regimes have been discussed and are supported by experiment. On the one hand it has been found that in some experiments Rayleigh scattering gives rise to negligible decoherence provided that the elastic scattering rates from both qubit levels are approximately equal [10]. On the other hand, decoherence due to Rayleigh scattering of photons on a cycling transition is used for strong projective state measurement [11].In this letter we develop a microscopic theory for the decoherence of a qubit due to elastic Rayleigh scattering that gives a unified treatment of these different regimes. Our key finding is that the decoherence induced by Rayleigh scattering is proportional to the square of the * Electronic address: huys@csir.co.za † Electronic address: john.bollinger@nist.gov difference of the probability amplitudes for elastic scattering from the two levels [Eq. (7)]. When the two amplitudes are approximately equal the resulting decoherence rate can be small (first case above) and when one amplitude dominates the other, Rayleigh decoherence c...

Anomalous light shift through quantum jumps in quasiresonant Rayleigh scattering

“…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.…”

“…We showed that the decoherence reported for a far-from-resonance drive in [2] evolves into an anomalous light shift (shift of opposite sign) when the scattering is quasi-resonant. The two effects are unified through their common mechanism, whereby phase is accumulated as quantum jumps map the ground state coherence when a photon is scattered.…”

“…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 trajectory simulations.…”

“…Uys et al [2] examined this case for far-off-resonance driving (δ − = −δ + ≫ γ/2). In this regime, A (−) /A (+) = −1, and each quantum jump shifts the phase of the superposition by π, leading to their reported decoherence.…”

Unitary cavity spin squeezing by quantum erasure

“…For Raman scattering, the state is encoded in the frequency of the scattered light. For Rayleigh scattering, it is encoded in the phase of the scattered field, because the laser detuning from resonance has opposite sign for the two spin states [46]. Any atom which scatters a photon into free space therefore acquires an unknown phase, entangled with the information lost in the scattered field and uncorrelated with that of the other atoms in the ensemble.…”