Amplifying Single-Photon Nonlinearity Using Weak Measurements

Abstract

We show that weak measurement can be used to "amplify" optical nonlinearities at the singlephoton level, such that the effect of one properly post-selected photon on a classical beam may be as large as that of many un-post-selected photons. We find that "weak-value amplification" offers a marked improvement in the signal-to-noise ratio in the presence of technical noise with long correlation times. Unlike previous weak-measurement experiments, our proposed scheme has no classical equivalent.An interaction between two independent photons could be used to serve as a "quantum logic gate," enabling the development of optical quantum computers [1][2][3], as well as opening up an essentially new field of quantum nonlinear optics [4]. Typical optical nonlinearities are many orders of magnitude too weak to create a π phase shift as required in initial proposals, but more recently it was realized that any phase shift large enough to be measured on a single shot could be leveraged into a quantum logic gate [5]. Much recent work has shown that atomic coherence effects [6][7][8][9] and nonlinearities in microstructured fiber [10,11] can generate greatly enhanced Kerr nonlinearities. While even a very small phase shift can be made larger than the quantum (shot) noise, by using a sufficiently intense probe, present experiments are limited by technical rather than quantum noise and difficult to carry out even with much averaging. For example, in Ref.[11], a phase shift of 10 −7 rad was measured by averaging over 3 × 10 9 classical pulses with singlephoton-level intensities. To date, no one has yet been able to observe the cross-Kerr effect induced by a single propagating photon on a second optical beam [12]. In this Letter, we show that using weak-value amplification (WVA) [13][14][15], a single photon can be made to "act like" many photons, and it is possible to amplify a cross-Kerr phase shift to an observable value, much larger than the intrinsic magnitude of the single-photon-level nonlinearity. In so doing, we also demonstrate quantitatively how WVA may improve the signal-to-noise ratio (SNR) in appropriate regimes, a result of broad general applicability to quantum metrology.Weak measurement is an exciting new approach to understanding quantum systems from a time-symmetric perspective, obtaining information from both their preparation and subsequent post-selection [16]. In the past several years, it has been widely studied to address foundational questions in quantum mechanics [17], as well as for its potential application to ultrasensitive measurements [14,15,18,19]. If a quantum system is coupled only weakly to a probe, then very little information may be obtained from a single measurement, and in compensation, this measurement disturbs the sys-

Short-pulse cross-phase modulation in an electromagnetically-induced-transparency medium

“…However, naturally occurring nonlinear optical coefficients are insufficient for these applications. Several different approaches have been taken to tackle the problem of very weak nonlinearities, including the use of photonic crystal fibres [5], Rydberg atoms [6][7][8][9], atoms in hollow-core fibers [10], single atoms coupled to microresonators [11] and even proposals to amplify the magnitude of existing nonlinear optical effects [12]. Schmidt and Imamoglu proposed a scheme [13] based on electromagnetically induced transparency (EIT) [14] which allowed for "giant", resonantly-enhanced optical nonlinearities while simultaneously eliminating absorption.…”

Pre- and postselected quantum states: Density matrices, tomography, and Kraus operators

“…The concept was also explored experimentally [6] and shown to be useful in a wide range of contexts, ranging from superluminal light propagations [7,8] to cavity QED [9]. More recently, weak measurements on post-selected states have found surprising applications in metrology, with the development of novel amplification techniques for precision measurements [10][11][12][13].In parallel, the ideas of pre-and post-selected systems were also developed from a conceptual point of view, leading to new ideas on the notion of time in quantum mechanics [14]. Previous work has considered the case of pure pre-and post-selected states, both direct products as well as states entangled between the preparation and post-selection.…”

Quantum Entanglement Concentration Based on Nonlinear Optics for Quantum Communications

“…With the help of weak measurement, it is possible to amplify a cross-Kerr phase shift to an observable value, as discussed by Feizpour et al. The phase shift is much larger than the intrinsic magnitude of the single-photon-level nonlinearity [107]. Recently, Zhu and Huang also showed that giant cross-Kerr nonlinearities can be obtained with nearly vanishing optical absorption, investigating the linear and nonlinear propagation of probe and signal pulses, which are coupled in a double-quantum-well structure with a four-level, double-type configuration [108].…”