Quantum-state-preserving optical frequency conversion and pulse reshaping by four-wave mixing

Abstract:We explore theoretically the feasibility of using frequency conversion by sum-or difference-frequency generation, enabled by threewave-mixing, for selectively multiplexing orthogonal input waveforms that overlap in time and frequency. Such a process would enable a drop device for use in a transparent optical network using temporally orthogonal waveforms to encode different channels. We model the process using coupled-mode equations appropriate for wave mixing in a uniform secondorder nonlinear optical medium pumped by a strong laser pulse. We find Green functions describing the process, and employ Schmidt (singularvalue) decompositions thereof to quantify its viability in functioning as a coherent waveform discriminator. We define a selectivity figure of merit in terms of the Schmidt coefficients, and use it to compare and contrast various parameter regimes via extensive numerical computations. We identify the most favorable regime (at least in the case of no pump chirp) and derive the complete analytical solution for the same. We bound the maximum achievable selectivity in this parameter space. We show that including a frequency chirp in the pump does not improve selectivity in this optimal regime. We also find an operating regime in which high-efficiency frequency conversion without temporal-shape selectivity can be achieved while preserving the shapes of a wide class of input pulses. The results are applicable to both classical and quantum frequency conversion.

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“…Fortunately, in this same regime the problem can be solved analytically, following [22](detailed in Appendix III). The exact GF is found to be…”

Section: Analytical Solution For Single Sideband Velocity Matched Regimementioning

confidence: 99%

Temporal mode selectivity by frequency conversion in second-order nonlinear optical waveguides

Reddy¹,

Raymer²,

McKinstrie³

et al. 2013

Opt. Express

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109

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“…Reshaping was also shown theoretically in the high-conversion regime [35]. However, none of these results included the effects of cross-(CPM) and self-phase modulation (SPM), collectively referred to as nonlinear phase modulation (NPM).…”

Section: Introductionmentioning

confidence: 98%

“…The results of the asymmetric collision are displayed in Fig. 5, withγ = 0.25 corresponding to a maximal conversion efficiency of 25 % for a complete collision [35]. Fig.…”

Section: Asymmetric Collisionsmentioning

confidence: 99%

Effects of nonlinear phase modulation on Bragg scattering in the low-conversion regime

Mejling¹,

Cargill²,

McKinstrie³

et al. 2012

Opt. Express

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Abstract:In this paper, we consider the effects of nonlinear phase modulation on frequency conversion by four-wave mixing (Bragg scattering) in the low-conversion regime. We derive the Green functions for this process using the time-domain collision method, for partial collisions, in which the four fields interact at the beginning or the end of the fiber, and complete collisions, in which the four fields interact at the midpoint of the fiber. If the Green function is separable, there is only one output Schmidt mode, which is free from temporal entanglement. We find that nonlinear phase modulation always chirps the input and output Schmidt modes and renders the Green function formally nonseparable. However, by pre-chirping the pumps, one can reduce the chirps of the Schmidt modes and enable approximate separability. Thus, even in the presence of nonlinear phase modulation, frequency conversion with arbitrary pulse reshaping is possible, as predicted previously [Opt. Express 20, 8367-8396 (2012)].

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“…In addition, by using photon-numberresolving (PNR) detectors, mode-resolved photon counting (MRPC) can be accomplished, based on which quantum statistics of high-dimensional photonic signals can be characterized on a mode-by-mode basis. Because the PM conditions can be engineered by tailoring the pump waves driving the QFC process, ultrafast manipulations and measurements of qud its are realizable in chip-scale devices with low transmission losses [8]. Our approach thus holds promise for use in practical applications of high-dimensional photonic signals.…”

mentioning

confidence: 99%

Mode-resolved photon counting via cascaded quantum frequency conversion

Huang

Kumar

2013

Opt. Lett.

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Resources for the manipulation and measurements of high-dimensional photonic signals are crucial for implementing qudit-based applications. Here we propose potentially high-performance, chip-compatible devices for such purposes by exploiting quantum-frequency conversion in nonlinear optical media. Specifically, by using sum-frequency generation in a χ (2) waveguide we show how mode-resolved photon counting can be accomplished for telecom-band photonic signals subtending multiple temporal modes. Our method is generally applicable to any nonlinear medium with arbitrary dispersion property. c 2013 Optical Society of America OCIS codes: 190.4410, 270.5290 Photonic signals are widely employed in many modern applications such as secure key generation, quantum computation, and near Holevo-capacity telecommunications [1]. In these applications, photons occupying low-dimensional Hilbert spaces composed of polarization or spatial degrees of freedom are most commonly used. Recently, the use of high-dimensional photonic signals, known as qud its, has attracted attention as they can offer significant advantages over qubits in terms of higher channel capacity, better information security, and so on. There have been quite a few proposals for using photonic qudits in applications such as secure telecommunications [2] and super-dense coding [3].Crucial to implementing the aforementioned quditbased applications are the capabilities for manipulating and measuring high-dimensional photonic signals. Existing solutions have been based on serializing multiple, linear, two-port optical devices [4] or using lossy spatialmode modulators [5]. Their performance in practice, particularly in large-d systems, will be highly inefficient due to the need for complicated experimental setups with high concomitant transmission losses.In this Letter, we study a potentially high efficiency, low-loss approach for manipulating and measuring photonic signals in high-dimensional Hilbert spaces composed of polarization, spatial, and temporal degrees of freedom. It is built on quantum-frequency conversion (QFC), a coherent process that can translate the carrier frequency (wavelength) of photonic signals without disturbing their quantum states, including any correlation or entanglement with other quantum objects [6]. It is well known that QFC in nonlinear media is efficient only for those appropriate combinations of wavelengths, spatiotemporal modes, and polarizations of the interacting light waves for which phase matching (PM) occurs. Thus it is possible to engineer the conditions for PM such that only photons in desired modes are frequency converted with high efficiency, while those in other modes remain unaffected [7]. By detecting the frequency-converted signals with ordinary single-photon detectors, differences in the photons' mode-profile details, which are otherwise difficult to monitor, can be precisely measured. In addition, by using photon-numberresolving (PNR) detectors, mode-resolved photon counting (MRPC) can be accomplished, based on which...

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Quantum-state-preserving optical frequency conversion and pulse reshaping by four-wave mixing

Cited by 53 publications

References 25 publications

Temporal mode selectivity by frequency conversion in second-order nonlinear optical waveguides

Temporal mode selectivity by frequency conversion in second-order nonlinear optical waveguides

Effects of nonlinear phase modulation on Bragg scattering in the low-conversion regime

Mode-resolved photon counting via cascaded quantum frequency conversion

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