Time reversal of arbitrary photonic temporal modes via nonlinear optical frequency conversion

Abstract

Single-photon wave packets can carry quantum information between nodes of a quantum network. An important general operation in photon-based quantum information systems is 'blind' reversal of a photon's temporal wave packet envelope, that is, the ability to reverse an envelope without knowing the temporal state of the photon. We present an all-optical means for doing so, using nonlinear-optical frequency conversion driven by a short pump pulse. The process used may be sum-frequency generation or four-wave Bragg scattering. This scheme allows for quantum operations such as a temporal-mode parity sorter. We also verify that the scheme works for arbitrary states (not only single-photon ones) of an unknown wave packet.

Input-output theory with time-reversal

“…(34), − (γ 2 /2 + iω 2 ) σ − 2 , we see that the γ 2 terms have opposite signs while the ω 2 terms have the same sign. Thus, as desired, σ− 1 (t) satisfies a timereversed equation in terms of its slowly varying envelope function as compared to σ − 2 (t) (we cannot time-reverse the fast oscillations [19]).…”

“…Transformations of this form are physically justified in Ref. 19, which uses the parameters α = −m > 0, ω 1 = ω s , and ω 2 = ω r . Consider the part of the field in Eq.…”

“…For the transformation to be causal the field must depend on past times, t ≥ t0 , such that t ≥ t s ≡ T /(1 + α), which defines the physical meaning of T . Physically, the transformation will be driven by a pump laser pulse of length L over a total integration time ∆ = L/c [19]. As the wave packet is broadened by α in the time domain the upper bound for the transformation is t ≤ t f ≡ t s + α∆.…”

“…This challenge can be dealt with using photon manipulation to transform the wave packet emitted by one system, tuning its spectral properties, so that it will be absorbed by another system. The relevant photon manipulations are optically reversing the temporal envelope of a photon wave packet, quantum frequency conversion, and pulse shaping [19][20][21].…”

Detecting two photons with one molecule

“…The idea that a quantum system absorbs a singlephoton wave packet with in principle 100% efficiency if and only if it is the time-reversed version of a photon that the system would emit if it started in the final state [40,41] does not apply so simply here, because of the presence of irreversible spontaneous decay. If we imagine we would apply a laser pulse to the |F 1 → |F 2 transition to induce stimulated emission, then, as is well known [42,43], that idea indeed would apply straightforwardly .…”