Quantum noise and superluminal propagation

Abstract

1 Abstract Causal "superluminal" effects have recently been observed and discussed in various contexts. The question arises whether such effects could be observed with extremely weak pulses, and what would prevent the observation of an "optical tachyon." Aharonov, Reznik, and Stern (ARS) [Phys. Rev. Lett. 81, 2190(1998 have argued that quantum noise will preclude the observation of a superluminal group velocity when the pulse consists of one or a few photons. In this paper we reconsider this question both in a general framework and in the specific example, suggested by Chiao, Kozhekin, and Kurizki [Phys. Rev. Lett. 77, 1254(1996], of off-resonant, short-pulse propagation in an optical amplifier. We derive in the case of the amplifier a signal-to-noise ratio that is consistent with the general ARS conclusions when we impose their criteria for distinguishing between superluminal propagation and propagation at the speed c. However, results consistent with the semiclassical arguments of CKK are obtained if weaker criteria are imposed, in which case the signal can exceed the noise without being "exponentially large." We show that the quantum fluctuations of the field considered by ARS are closely related to superfluorescence noise. More generally we consider the implications of unitarity for superluminal propagation and quantum noise and study, in addition to the complete and truncated wavepackets considered by ARS, the residual wavepacket formed by their difference. This leads to the conclusion that the noise is mostly luminal and delayed with respect to the superluminal signal. In the limit of a very weak incident signal pulse, the superluminal signal will be dominated by the noise part, and the signal-to-noise ratio will therefore be very small.

Bounds and enhancements for negative scattering time delays

“…Many of these works have discussed the relativistic or "Einstein causality" principle, i.e., the limiting role of the velocity of light in the transmission of signals [13,14,15,16,17,18,19], which must be applicable to relativistic wave equations; the influence of the different wavepacket regions (rear, front) in the transmitted signal, also in the non-relativistic case [20]; the attainability of a sensible signal to noise ratio in superluminal experiments with a small number of photons [21,22,23]; or the role of the frequency band limitation of the signals [24,25,26,27,28]. Much less attention has been paid to the consequences of the more primitive and general causality principle stating that "the effect cannot precede the cause".…”

“…[59] For limitations of superluminal propagation due to quantum fluctuations in systems with inverted atomic population see [21,22,23]; the Hartman effect is also affected by dissipation or absorption [53,54] [60] We could try to avoid the interpretational pitfalls of the extrapolated phase time and look instead at the time t out a for a wave packet initially localized near the left edge of the barrier, and with a small spatial width compared to the barrier length d = 2a. In this way one might identify the entrance time and the preparation instant at t = 0 with a tolerable small uncertainty.…”

Assessing Potential Propulsion Breakthroughs

“…Experimental and theoretical work indicates that the information transfer rate is only apparently superluminal, with no causality violations. Although the leading edge of the signal does appear to make it through the barrier faster, the entire signal is still light-speed limited [Mojahedi 2000a, 2000b, and Segev 2000. This topic still serves, however, as a tool to explore this intriguing aspect of physics.…”

Quantum noise of a white-light cavity using a double-pumped gain medium

“…The gain medium with anomalous dispersion is subject to an additional quantum noise that accompanies the amplification process. The effect of this additional quantum noise on the observability of "superluminal" pulse propagation effect has been discussed in [17][18][19][20]. In particular, Refs.…”

“…[17,20] gave a general discussion of this noise using Caves' theory of the amplifier [21], which based on the general requirement that the field operator should satisfy bosonic commutation relation, without providing a complete analysis of the dynamical origin of this noise. Reference [19] discussed a more concrete example of the field propagation inside a medium consisting of pumped two-level atoms. However, the effect of this additional noise on the sensitivity of the gravitational wave detector designs proposed in [9][10][11][12][13] was not analyzed before.…”