Translation of quantum states by four-wave mixing in fibers

NOON-state interference in the frequency domain

The examination of entanglement across various degrees of freedom has been pivotal in augmenting our understanding of fundamental physics, extending to high dimensional quantum states, and promising the scalability of quantum technologies. In this paper, we demonstrate the photon number path entanglement in the frequency domain by implementing a frequency beam splitter that converts the single-photon frequency to another with 50% probability using Bragg scattering four-wave mixing. The two-photon NOON state in a single-mode fiber is generated in the frequency domain, manifesting the two-photon interference with two-fold enhanced resolution compared to that of single-photon interference, showing the outstanding stability of the interferometer. This successful translation of quantum states in the frequency domain will pave the way toward the discovery of fascinating quantum phenomena and scalable quantum information processing.

Spectral control of nonclassical light pulses using an integrated thin-film lithium niobate modulator

Manipulating the frequency and bandwidth of nonclassical light is essential for implementing frequency-encoded/multiplexed quantum computation, communication, and networking protocols, and for bridging spectral mismatch among various quantum systems. However, quantum spectral control requires a strong nonlinearity mediated by light, microwave, or acoustics, which is challenging to realize with high efficiency, low noise, and on an integrated chip. Here, we demonstrate both frequency shifting and bandwidth compression of heralded single-photon pulses using an integrated thin-film lithium niobate (TFLN) phase modulator. We achieve record-high electro-optic frequency shearing of telecom single photons over terahertz range (±641 GHz or ±5.2 nm), enabling high visibility quantum interference between frequency-nondegenerate photon pairs. We further operate the modulator as a time lens and demonstrate over eighteen-fold (6.55 nm to 0.35 nm) bandwidth compression of single photons. Our results showcase the viability and promise of on-chip quantum spectral control for scalable photonic quantum information processing.

Ultratunable Quantum Frequency Conversion in Photonic Crystal Fiber

Quantum frequency conversion of single photons between wavelength bands is a key enabler to realizing widespread quantum networks. We demonstrate the quantum frequency conversion of a heralded 1551 nm photon to any wavelength within an ultrabroad (1226-1408 nm) range in a group-velocity-symmetric photonic crystal fiber, covering over 150 independent frequency bins. The target wavelength is controlled by tuning only a single pump laser wavelength. We find internal, and total, conversion efficiencies of 12(1)% and 1.4(2)%, respectively. For the case of converting 1551 to 1300 nm we measure a heralded g^{(2)}(0)=0.25(6) for converted light from an input with g^{(2)}(0)=0.034(8). We expect that this photonic crystal fiber can be used for myriad quantum networking tasks.

Toward a Quantum Memory in a Fiber Cavity Controlled by Intracavity Frequency Translation

We propose a quantum memory protocol based on trapping photons in a fiber-integrated cavity, comprised of a birefringent fiber with dichroic reflective end facets. Photons are switched into resonance with the fiber cavity by intracavity Bragg-scattering frequency translation, driven by ancillary control pulses. After the storage delay, photons are switched out of resonance with the cavity, again by intracavity frequency translation. We demonstrate storage of quantum-level THz-bandwidth coherent states for a lifetime up to 16 cavity round trips, or 200 ns, and a maximum overall efficiency of 73%.

An integrated photonic circuit for color qubit preparation by third-order nonlinear interactions

This work presents a feasible design of an integrated photonic circuit performing as a device for single-qubit preparation and rotations through the third-order nonlinear process of difference frequency generation (DFG) and defined in the temporal mode basis. The first stage of our circuit includes the generation of heralded single photons by spontaneous four-wave mixing in a micro-ring cavity engineered for delivering a single-photon state in a unique temporal mode. The second stage comprises the implementation of DFG in a spiral waveguide with controlled dispersion properties for reaching color qubit preparation fidelity close to unity. We present the generalized rotation operator related to the DFG process, a methodology for the device design, and qubit preparation fidelity results as a function of user-accessible parameters.

Nonreciprocal Frequency Domain Beam Splitter

The canonical beam splitter-a fundamental building block of quantum optical systems-is a reciprocal element. It operates on forward- and backward-propagating modes in the same way, regardless of direction. The concept of nonreciprocal quantum photonic operations, by contrast, could be used to transform quantum states in a momentum- and direction-selective fashion. Here we demonstrate the basis for such a nonreciprocal transformation in the frequency domain through intermodal Bragg scattering four-wave mixing (BSFWM). Since the total number of idler and signal photons is conserved, the process can preserve coherence of quantum optical states, functioning as a nonreciprocal frequency beam splitter. We explore the origin of this nonreciprocity and find that the phase-matching requirements of intermodal BSFWM produce an enormous asymmetry (76×) in the conversion bandwidths for forward and backward configurations, yielding ∼25  dB of nonreciprocal contrast over several hundred GHz. We also outline how the demonstrated efficiencies (∼10^{-4}) may be scaled to near-unity values with readily accessible powers and pumping configurations for applications in integrated quantum photonics.

Tunable frequency matching for efficient four-wave-mixing Bragg scattering in microrings

We propose and theoretically study a tunable frequency matching method for four-wave-mixing Bragg-scattering frequency conversion in microring resonators. A tunable coupling between the clockwise and counterclockwise propagating modes in the resonators was designed to introduce adjustable mode splitting, thus compensating for the frequency mismatching under different wavelengths. Using a silicon nitride ring resonator as an example, we showed that the tuning bandwidth approaches 35 number of FSRs. Numerical simulations further revealed that the phase-matching strategy is valid under different wavelength combinations and is robust to variations in waveguide geometry and fabrication. These results suggest promising applications in high-efficiency frequency conversion, integrated nonlinear photonics, and quantum optics.

Quantum frequency conversion of vacuum squeezed light to bright tunable blue squeezed light and higher-order spatial modes

Quantum frequency conversion, the process of shifting the frequency of an optical quantum state while preserving quantum coherence, can be used to produce non-classical light at otherwise unapproachable wavelengths. We present experimental results based on highly efficient sum-frequency generation (SFG) between a vacuum squeezed state at 1064 nm and a tunable pump source at 850 nm ± 50 nm for the generation of bright squeezed light at 472 nm ± 4 nm, currently limited by the phase-matching of the used nonlinear crystal. We demonstrate that the SFG process conserves part of the quantum coherence as a 4.2(±0.2) dB 1064 nm vacuum squeezed state is converted to a 1.6(±0.2) dB tunable bright blue squeezed state. We furthermore demonstrate simultaneous frequency- and spatial-mode conversion of the 1064-nm vacuum squeezed state, and measure 1.1(±0.2) dB and 0.4(±0.2) dB of squeezing in the TEM₀₁ and TEM₀₂ modes, respectively. With further development, we foresee that the source may find use within fields such as sensing, metrology, spectroscopy, and imaging.

Single Photon Frequency Conversion for Frequency Multiplexed Quantum Networks in the Telecom Band

High-speed long-range quantum communication requires combining frequency multiplexed photonic channels with quantum memories. We experimentally demonstrate an integrated quantum frequency conversion protocol that can convert between wavelength division multiplexing channels in the telecom range with an efficiency of 55±8% and a noise subtracted Hong-Ou-Mandel (HOM) dip visibility of 84.5%. This protocol is based on a cascaded second order nonlinear interaction and can be used to interface a broad spectrum of frequencies with narrowband quantum memories, or alternatively as a quantum optical transponder, efficiently interfacing different regions of a frequency-multiplexed spectrum.

Hybrid III-V diamond photonic platform for quantum nodes based on neutral silicon vacancy centers in diamond

Integrating atomic quantum memories based on color centers in diamond with on-chip photonic devices would enable entanglement distribution over long distances. However, efforts towards integration have been challenging because color centers can be highly sensitive to their environment, and their properties degrade in nanofabricated structures. Here, we describe a heterogeneously integrated, on-chip, III-V diamond platform designed for neutral silicon vacancy (SiV⁰) centers in diamond that circumvents the need for etching the diamond substrate. Through evanescent coupling to SiV⁰ centers near the surface of diamond, the platform will enable Purcell enhancement of SiV⁰ emission and efficient frequency conversion to the telecommunication C-band. The proposed structures can be realized with readily available fabrication techniques.

Proposal for noise-free visible-telecom quantum frequency conversion through third-order sum and difference frequency generation

Quantum frequency conversion (QFC) between the visible and telecom is a key to connect quantum memories in fiber-based quantum networks. Current methods for linking such widely separated frequencies, such as sum/difference frequency generation and four-wave mixing Bragg scattering, are prone to broadband noise generated by the pump laser(s). To address this issue, we propose to use third-order sum/difference frequency generation (TSFG/TDFG) for an upconversion/downconversion QFC interface. In this process, two long wavelength pump photons combine their energy and momentum to mediate frequency conversion across the large spectral gap between the visible and telecom bands, which is particularly beneficial from the noise perspective. We show that waveguide-coupled silicon nitride microring resonators can be designed for efficient QFC between 606 and 1550 nm via a 1990 nm pump through TSFG/TDFG. We simulate the device dispersion and coupling, and from the simulated parameters, estimate that the frequency conversion can be efficient (${\gt}80 \%$) at 50 mW pump power. Our results suggest that microresonator TSFG/TDFG is promising for compact, scalable, and low-power QFC across large spectral gaps.

Resource-efficient frequency conversion for quantum networks via sequential four-wave mixing

We report a resource-efficient scheme in which a single pump laser was used to achieve frequency conversion by Bragg-scattering four-wave mixing in a photonic crystal fiber. We demonstrate bidirectional conversion of coherent light between Sr⁺²P_1/2→²D_3/2 emission wavelength at 1092 nm and the telecommunication C band with conversion efficiencies of 4.2% and 37% for up- and down-conversion, respectively. We discuss how the scheme may be viably scaled to meet the temporal, spectral, and polarization stability requirements of a hybrid light-matter quantum network.

Controlled-Phase Gate Using Dynamically Coupled Cavities and Optical Nonlinearities

We show that relatively simple integrated photonic circuits have the potential to realize a high fidelity deterministic controlled-phase gate between photonic qubits using bulk optical nonlinearities. The gate is enabled by converting travelling continuous-mode photons into stationary cavity modes using strong classical control fields that dynamically change the effective cavity-waveguide coupling rate. This architecture succeeds because it reduces the wave packet distortions that otherwise accompany the action of optical nonlinearities [J. Shapiro, Phys. Rev. A 73, 062305 (2006)PLRAAN1050-294710.1103/PhysRevA.73.062305; J. Gea-Banacloche, Phys. Rev. A 81, 043823 (2010)PLRAAN1050-294710.1103/PhysRevA.81.043823]. We show that high-fidelity gates can be achieved with self-phase modulation in χ^{(3)} materials as well as second-harmonic generation in χ^{(2)} materials. The gate fidelity asymptotically approaches unity with increasing storage time for an incident photon wave packet with fixed duration. We also show that dynamically coupled cavities enable a trade-off between errors due to loss and wave packet distortion. Our proposed architecture represents a new approach to practical implementation of quantum gates that is room-temperature compatible and only relies on components that have been individually demonstrated.

Observation of Rapid Adiabatic Passage in Optical Four-Wave Mixing

We observe clear evidence of adiabatic passage between photon populations via a four-wave mixing process, implemented through a dispersion sweep arranged by a core diameter taper of an optical fiber. Photonic rapid adiabatic passage through the cubic electric susceptibility thus opens precise control of frequency translation between broadband light fields to all common optical media. Areas of potential impact include optical fiber and on-chip waveguide platforms for quantum information, ultrafast spectroscopy and metrology, and extreme light-matter interaction science.

Frequency-Domain Quantum Interference with Correlated Photons from an Integrated Microresonator

Frequency encoding of quantum information together with fiber and integrated photonic technologies can significantly reduce the complexity and resource requirements for realizing all-photonic quantum networks. The key challenge for such frequency domain processing of single photons is to realize coherent and selective interactions between quantum optical fields of different frequencies over a range of bandwidths. Here, we report frequency-domain Hong-Ou-Mandel interference with spectrally distinct photons generated from a chip-based microresonator. We use four-wave mixing to implement an active "frequency beam splitter" and achieve interference visibilities of 0.95±0.02. Our work establishes four-wave mixing as a tool for selective high-fidelity two-photon operations in the frequency domain which, combined with integrated single-photon sources, provides a building block for frequency-multiplexed photonic quantum networks.

A universal frequency engineering tool for microcavity nonlinear optics: multiple selective mode splitting of whispering-gallery resonances

Whispering-gallery microcavities have been used to realize a variety of efficient parametric nonlinear optical processes through the enhanced light-matter interaction brought about by supporting multiple high quality factor and small modal volume resonances. Critical to such studies is the ability to control the relative frequencies of the cavity modes, so that frequency matching is achieved to satisfy energy conservation. Typically this is done by tailoring the resonator cross-section. Doing so modifies the frequencies of all of the cavity modes, that is, the global dispersion profile, which may be undesired, for example, in introducing competing nonlinear processes. Here, we demonstrate a frequency engineering tool, termed multiple selective mode splitting (MSMS), that is independent of the global dispersion and instead allows targeted and independent control of the frequencies of multiple cavity modes. In particular, we show controllable frequency shifts up to 0.8 nm, independent control of the splitting of up to five cavity modes with optical quality factors ≳ 105, and strongly suppressed frequency shifts for untargeted modes. The MSMS technique can be broadly applied to a wide variety of nonlinear optical processes across different material platforms, and can be used to both selectively enhance processes of interest and suppress competing unwanted processes.

Quantum Frequency Conversion of a Quantum Dot Single-Photon Source on a Nanophotonic Chip

Single self-assembled InAs/GaAs quantum dots are promising bright sources of indistinguishable photons for quantum information science. However, their distribution in emission wavelength, due to inhomogeneous broadening inherent to their growth, has limited the ability to create multiple identical sources. Quantum frequency conversion can overcome this issue, particularly if implemented using scalable chip-integrated technologies. Here, we report the first demonstration of quantum frequency conversion of a quantum dot single-photon source on a silicon nanophotonic chip. Single photons from a quantum dot in a micropillar cavity are shifted in wavelength with an on-chip conversion efficiency ≈ 12 %, limited by the linewidth of the quantum dot photons. The intensity autocorrelation function g ( 2 ) ( τ ) for the frequency-converted light is antibunched with g ( 2 ) ( 0 ) = 0.290 ± 0.030 , compared to the before-conversion value g ( 2 ) ( 0 ) = 0.080 ± 0.003 . We demonstrate the suitability of our frequency conversion interface as a resource for quantum dot sources by characterizing its effectiveness across a wide span of input wavelengths (840 nm to 980 nm), and its ability to achieve tunable wavelength shifts difficult to obtain by other approaches.

Adiabatic four-wave mixing frequency conversion

We introduce the concept of adiabatic four-wave mixing (AFMW) frequency conversion in cubic nonlinear media through an analogy to dynamics in quantum two-level systems. Rapid adiabatic passage in four-wave mixing enables coherent near-100% photon number down-conversion or up-conversion over a bandwidth much larger than ordinary phase-matching bandwidths, overcoming the normal efficiency-bandwidth trade-off. We develop numerical methods to simulate AFWM pulse propagation in silicon photonics and fiber platforms as examples. First, we show that with a longitudinally varying silicon waveguide structure, a bandwidth of 70 nm centered at 1820 nm can be generated with 90% photon number conversion. Second, we predict the broadband generation of nanojoule energy, 4.2-5.2 μm mid-infrared light in a short, linearly tapered fluoride step-index fiber. We expect the AFWM concept to be broadly applicable to cubic nonlinear platforms, for applications as diverse as bright ultrafast light pulse generation, sensing, and conversion between telecommunications bands.

Enhanced-contrast optical readout in ultrafast broadband Raman quantum memories

The signal-to-noise contrast of the optical readout in broadband Raman quantum memories is analyzed as a function of the pulse widths and phase properties of tailored optical field waveforms used to write in and read out broadband photon wave packets. Based on this analysis, we quantify the tradeoff between the readout contrast and the speed of such memories. Off-resonance coherent four-wave mixing is shown to provide a source of noise photons, lowering the readout contrast in broadband Raman quantum memories. This noise cannot be suppressed by phase matching, but can be radically reduced with a suitable polarization arrangement and proper field-waveform tailoring.

Surpassing the tuning speed limit of slow-light-based tunable optical delay via four-wave mixing Bragg scattering

We demonstrate a tunable optical delay that surpasses the tuning speed limit of the conventional slow-light-based optical delay. A novel nonlinear optical coupler, implemented by the four-wave mixing (FWM) Bragg scattering process, is utilized to perform destructive interference of the slow-light delayed signal pulse and a nondelayed reference pulse. As a result, the Brillouin-induced frequency-dependent phase shift, as well as the group delay of the synthesized pulse, is amplified. The group delay amplification factor, determined by the coupling ratio of the nonlinear optical coupler, can be tuned through varying the FWM pump power to provide an ultrafast response. Our experimental result demonstrates that an initial 6.2 ns Brillouin-induced optical delay can be amplified and rapidly tuned within the range of -5.2 to 27.2 ns.

Shape-preserving and unidirectional frequency conversion by four-wave mixing

In this work, we investigate the properties of four-wave mixing Bragg scattering driven by orthogonally polarized pumps in a birefringent waveguide. This configuration enables a large signal conversion bandwidth, and allows strongly unidirectional frequency conversion as undesired Bragg-scattering processes are suppressed by waveguide birefringence. Moreover, we show that this form of Bragg scattering preserves the (arbitrary) signal pulse shape, even when driven by pulsed pumps.

Frequency multiplexing for quasi-deterministic heralded single-photon sources

Parametric single-photon sources are well suited for large-scale quantum networks due to their potential for photonic integration. Active multiplexing of photons can overcome the intrinsically probabilistic nature of these sources, resulting in near-deterministic operation. However, previous implementations using spatial and temporal multiplexing scale unfavorably due to rapidly increasing switching losses. Here, we break this limitation via frequency multiplexing in which switching losses remain fixed irrespective of the number of multiplexed modes. We use low-noise optical frequency conversion for efficient frequency switching and demonstrate multiplexing of three modes. We achieve a generation rate of 4.6 × 10⁴ photons per second with an ultra-low g⁽²⁾(0) = 0.07 indicating high single-photon purity. Our scalable, all-fiber multiplexing system has a total loss of just 1.3 dB, such that the 4.8 dB multiplexing enhancement markedly overcomes switching loss. Our approach offers a promising path to creating a deterministic photon source on an integrated chip-based platform.

The aim of multiplexing is to boost capabilities of probabilistic single photon sources, but is vexed by rapidly increasing switching losses. Here, the authors propose and implement an in-fiber frequency-multiplexing scheme where total losses are independent of the number of multiplexed modes.

Quantum temporal imaging by four-wave mixing

We investigate temporal imaging of broadband squeezed light by four-wave-mixing. We consider two possible imaging configurations: phase-conjugating (PC) and phase-preserving (PP). Both of these configurations have been successfully used for temporal imaging of classical temporal waveforms. We demonstrate that for quantum temporal imaging, precisely, temporal imaging of broadband squeezed light, these two schemes have very different behavior: the PC configuration deteriorates squeezing, while the PP configuration leaves it intact. These results are very important for the applications of temporal imaging for quantum communications and quantum information processing.

Phase matching as a gate for photon entanglement

Phase matching is shown to provide a tunable gate that helps discriminate entangled states of light generated by four-wave mixing (FWM) in optical fibers against uncorrelated photons originating from Raman scattering. Two types of such gates are discussed. Phase-matching gates of the first type are possible in the normal dispersion regime, where FWM sidebands can be widely tuned by high-order dispersion management, enhancing the ratio of the entangled-photon output to the Raman noise. The photon-entanglement gates of the second type are created by dual-pump cross-phase-modulation-induced FWM sideband generation and can be tuned by group-velocity mismatch of the pump fields.

Mach-Zehnder interferometer using frequency-domain beamsplitter

We demonstrate a first-order interference between coherent light at 1580 nm and 795 nm by using a frequency-domain Mach-Zehnder interferometer (MZI). The MZI is implemented by two frequency-domain BSs based on a second-order nonlinear optical effect in a periodically-poled lithium niobate waveguide with a strong pump light. The observed visibility is over 0.99 at 50% conversion efficiencies of the BSs. Toward photonic quantum information processing, sufficiently small background photon rate is necessary. From measurement results with a superconducting single photon detector (SSPD), we discuss the feasibility of the frequency-domain MZI in a quantum regime. Our estimation shows that the single photon interference with the visibility above 0.9 is feasible with practical settings.

Uni-directional wavelength conversion in silicon using four-wave mixing driven by cross-polarized pumps

We demonstrate optical frequency conversion between telecom wavelengths using four-wave mixing Bragg scattering powered by two pump pulses polarized on orthogonal axes of a silicon waveguide. This allows conversion in a single frequency direction while, with co-polarized pumps, the signal is redshifted or blueshifted with similar efficiency. Our approach exploits the birefringence of the waveguide and its effect on the phase matching of the four-wave mixing process. The blue or red direction can be selected by the input polarization of the signal, and 20 dB extinction ratios are observed with the unintended direction. This technique will allow efficient and controlled conversion between specified wavelength channels in integrated photonic devices.

Four-wave mixing Bragg scattering in hydrogenated amorphous silicon waveguides

We demonstrate 15% on-chip conversion efficiency of four-wave mixing Bragg scattering in a hydrogenated amorphous silicon waveguide with only 55 and 194 mW peak pump powers in the waveguide. The lightwaves can be maintained in the telecommunication band, and the operational bandwidth is measured to be larger than 4 nm.

Effects of Raman scattering and attenuation in silica fiber-based parametric frequency conversion

Four-wave mixing in the form of Bragg scattering (BS) has been predicted to enable quantum noise-less frequency conversion by analytic quantum approaches. Using a semi-classical description of quantum noise that accounts for loss and stimulated and spontaneous Raman scattering, which are not currently described in existing quantum approaches, we quantify the impacts of these effects on the conversion efficiency and on the quantum noise properties of BS in terms of an induced noise figure (NF). We give an approximate closed-form expression for the BS conversion efficiency that includes loss and stimulated Raman scattering, and we derive explicit expressions for the Raman-induced NF from the semi-classical approach used here. We find that Raman scattering induces a NF in the BS process that is comparable to the 3-dB NF associated with linear amplifiers.

Ion-photon entanglement and quantum frequency conversion with trapped Ba+ ions

Trapped ions are excellent candidates for quantum nodes, as they possess many desirable features of a network node including long lifetimes, on-site processing capability, and production of photonic flying qubits. However, unlike classical networks in which data may be transmitted in optical fibers and where the range of communication is readily extended with amplifiers, quantum systems often emit photons that have a limited propagation range in optical fibers and, by virtue of the nature of a quantum state, cannot be noiselessly amplified. Here, we first describe a method to extract flying qubits from a Ba⁺ trapped ion via shelving to a long-lived, low-lying D-state with higher entanglement probabilities compared with current strong and weak excitation methods. We show a projected fidelity of ≈89% of the ion-photon entanglement. We compare several methods of ion-photon entanglement generation, and we show how the fidelity and entanglement probability varies as a function of the photon collection optic's numerical aperture. We then outline an approach for quantum frequency conversion of the photons emitted by the Ba⁺ ion to the telecommunication range for long-distance networking and to 780 nm for potential entanglement with rubidium-based quantum memories. Our approach is significant for extending the range of quantum networks and for the development of hybrid quantum networks compromised of different types of quantum memories.

Low control-power wavelength conversion on a silicon chip

We demonstrate controlled wavelength conversion on a silicon chip based on four-wave mixing Bragg scattering (FWM-BS). A total conversion efficiency of 5% is achieved with strongly unbalanced pumps and a controlling peak power of 55 mW, while the efficiency is over 15% when using less asymmetric pumps. The numerical simulation agrees with the experimental results. Both time domain and spectral domain noise measurements show as low as 2 dB signal-to-noise ratio (SNR) penalty because of the strong pump noise, two-photon absorption, and free-carrier absorption in silicon. We discuss how the scheme can be used to implement an all-optically controlled high-speed switch.

High-speed all-optical NAND/AND logic gates using four-wave mixing Bragg scattering

A high-speed all-optical NAND logic gate is proposed and experimentally demonstrated using four-wave mixing Bragg scattering in highly nonlinear fiber. NAND/AND logic functions are implemented at two wavelengths by encoding logic inputs on two pumps via on-off keying. A 15.2-dB depletion of the signal is obtained for NAND operation, and time domain measurements show 10-Gb/s NAND/AND logic operations with open eye diagrams. The approach can be readily extended to higher data rates and transferred to on-chip waveguide platforms.

Coherent coupling between radio frequency, optical, and acoustic waves in piezo-optomechanical circuits

Optomechanical cavities have been studied for applications ranging from sensing to quantum information science. Here, we develop a platform for nanoscale cavity optomechanical circuits in which optomechanical cavities supporting co-localized 1550 nm photons and 2.4 GHz phonons are combined with photonic and phononic waveguides. Working in GaAs facilitates manipulation of the localized mechanical mode either with a radio frequency (RF) field through the piezo-electric effect, which produces acoustic waves that are routed and coupled to the optomechanical cavity by phononic crystal waveguides, or optically through the strong photoelastic effect. Along with mechanical state preparation and sensitive readout, we use this to demonstrate an acoustic wave interference effect, similar to atomic coherent population trapping, in which RF-driven coherent mechanical motion is cancelled by optically-driven motion. Manipulating cavity optomechanical systems with equal facility through both photonic and phononic channels enables new architectures for signal transduction between the optical, electrical, and mechanical domains.

Frequency translation via four-wave mixing Bragg scattering in Rb filled photonic bandgap fibers

We demonstrate frequency translation at microwatt pump power levels in Rubidium vapor confined to a hollow-core photonic bandgap fiber using four-wave mixing Bragg scattering. The 5S(1/2)→5D(3/2) two-photon transition in 85Rb is employed for the four-wave mixing process. Using continuous-wave pump beams at 780 and 795 nm, a weak signal beam at 776 nm is translated to a wavelength of 762 nm with a 21% conversion efficiency at pump powers of 300 μW.

Raman and loss induced quantum noise in depleted fiber optical parametric amplifiers

We present a semi-classical approach for predicting the quantum noise properties of fiber optical parametric amplifiers. The unavoidable contributors of noise, vacuum fluctuations, loss-induced noise, and spontaneous Raman scattering, are included in the analysis of both phase-insensitive and phase-sensitive amplifiers. We show that the model agrees with earlier fully quantum approaches in the linear gain regime, whereas in the saturated gain regime, in which the classical equations are valid, we predict that the amplifier increases the signal-to-noise ratio by generating an amplitude-squeezed state of light. Also, in the same process, we analyze the quantum noise properties of the pump, which is difficult using standard quantum approaches, and we discover that the pump displays complicated dynamics in both the linear and the nonlinear gain regimes.

A chip-scale, telecommunications-band frequency conversion interface for quantum emitters

We describe a chip-scale, telecommunications-band frequency conversion interface designed for low-noise operation at wavelengths desirable for common single photon emitters. Four-wave-mixing Bragg scattering in silicon nitride waveguides is used to demonstrate frequency upconversion and downconversion between the 980 nm and 1550 nm wavelength regions, with signal-to-background levels > 10 and conversion efficiency of ≈ -60 dB at low continuous wave input pump powers (< 50 mW). Finite element simulations and the split-step Fourier method indicate that increased input powers of ≈ 10 W (produced by amplified nanosecond pulses, for example) will result in a conversion efficiency > 25 % in existing geometries. Finally, we present waveguide designs that can be used to connect shorter wavelength (637 nm to 852 nm) quantum emitters with 1550 nm.

Quantum frequency conversion in nonlinear microcavities

We study nonlinear microresonantors as potential implements for quantum frequency conversion of narrowband optical signals. Using silicon-nitride microdisks as a concrete example, we show that high-conversion performance can be achieved with relatively low pump power. Being chip integratable, such devices hold promise for use in large-scale quantum applications, including atomic-memory-based quantum repeaters.

Phase-sensitive amplification of light in a χ(3) photonic chip using a dispersion engineered chalcogenide ridge waveguide

We report phase-sensitive amplification of light using χ((3)) parametric processes in a chalcogenide ridge waveguide. By spectrally slicing pump, signal and idler waves from a single pulsed source, we are able to observe 9.9 dB of on-chip phase-sensitive extinction with a signal-degenerate dual pump four-wave mixing architecture in good agreement with numerical simulations.

High-efficiency frequency conversion in the single-photon regime

In this Letter we demonstrate frequency conversion in the single-photon regime through Bragg-scattering four-wave mixing with near-unit efficiency in a 750 m long commercially available dispersion-engineered highly nonlinear fiber, where all photons and pump laser frequencies are in the low-loss telecommunications band. We achieve 99.1%±4.9% downconversion and 98.0%±5.0% upconversion of photons by 12 nm using a weak coherent state with an average input of 0.27 photons per detection gate window.

Low-noise chip-based frequency conversion by four-wave-mixing Bragg scattering in SiN(x) waveguides

Low-noise, tunable wavelength-conversion through nondegenerate four-wave mixing Bragg scattering in SiN(x) waveguides is experimentally demonstrated. Finite element method simulations of waveguide dispersion are used with the split-step Fourier method to predict device performance. Two 1550 nm wavelength band pulsed pumps are used to achieve tunable conversion of a 980 nm signal over a range of 5 nm with a peak conversion efficiency of ≈5%. The demonstrated Bragg scattering process is suitable for frequency conversion of quantum states of light.

Quantum frequency translation by four-wave mixing in a fiber: low-conversion regime

In this paper we consider frequency translation enabled by Bragg scattering, a four-wave mixing process. First we introduce the theoretical background of the Green function formalism and the Schmidt decomposition. Next the Green functions for the low-conversion regime are derived perturbatively in the frequency domain, using the methods developed for three-wave mixing, then transformed to the time domain. These results are also derived and verified using an alternative time-domain method, the results of which are more general. For the first time we include the effects of convecting pumps, a more realistic assumption, and show that separability and arbitrary reshaping is possible. This is confirmed numerically for Gaussian pumps as well as higher-order Hermite-Gaussian pumps.

Simultaneous frequency conversion, regeneration and reshaping of optical signals

Nondegenerate four-wave mixing in fibers enables the tunable and low-noise frequency conversion of optical signals. This paper shows that four-wave mixing driven by pulsed pumps can also regenerate and reshape optical signal pulses arbitrarily.

Theory of quantum frequency translation of light in optical fiber: application to interference of two photons of different color

We study quantum frequency translation and two-color photon interference enabled by the Bragg scattering four-wave mixing process in optical fiber. Using realistic model parameters, we computationally and analytically determine the Green function and Schmidt modes for cases with various pump-pulse lengths. These cases can be categorized as either "non-discriminatory" or "discriminatory" in regards to their propensity to exhibit high-efficiency translation or high-visibility two-photon interference for many different shapes of input wave packets or for only a few input wave packets, respectively. Also, for a particular case, the Schmidt mode set was found to be nearly equal to a Hermite-Gaussian function set. The methods and results also apply with little modification to frequency conversion by sum-frequency conversion in optical crystals.

Bragg scattering in a positive β4 fiber

The phase-matching curves for the four-wave mixing effect of Bragg scattering in two fibers with opposite sign β(4) dispersion coefficients have been measured experimentally. The measured phase-matching curves are in good agreement with theoretical expectations, and their dependence on several key parameters has been determined.

Field-quadrature and photon-number correlations produced by parametric processes

In a previous paper [Opt. Express 13, 4986 (2005)], formulas were derived for the field-quadrature and photon-number variances produced by multiple-mode parametric processes. In this paper, formulas are derived for the quadrature and number correlations. The number formulas are used to analyze the properties of basic devices, such as two-mode amplifiers, attenuators and frequency convertors, and composite systems made from these devices, such as cascaded parametric amplifiers and communication links. Amplifiers generate idlers that are correlated with the amplified signals, or correlate pre-existing pairs of modes, whereas attenuators decorrelate pre-existing modes. Both types of device modify the signal-to-noise ratios (SNRs) of the modes on which they act. Amplifiers decrease or increase the mode SNRs, depending on whether they are operated in phase-insensitive (PI) or phase-sensitive (PS) manners, respectively, whereas attenuators always decrease these SNRs. Two-mode PS links are sequences of transmission fibers (attenuators) followed by two-mode PS amplifiers. Not only do these PS links have noise figures that are 6-dB lower than those of the corresponding PI links, they also produce idlers that are (almost) completely correlated with the signals. By detecting the signals and idlers, one can eliminate the effects of electronic noise in the detectors.

Quantum frequency translation of single-photon states in a photonic crystal fiber

We experimentally demonstrate frequency translation of a nonclassical optical field via four-wave mixing (Bragg-scattering process) in a photonic crystal fiber (PCF). The high nonlinearity and the ability to control dispersion in PCF enable efficient translation between nearby photon channels within the visible to-near-infrared spectral range, useful in quantum networks. Heralded single photons at 683 nm were translated to 659 nm with an efficiency of 28.6±2.2 percent. Second-order correlation measurements on the 683- and 659-nm fields yielded g(683)(2) (0)=0.21±0.02 and g(659)(2) (0)=0.19±0.05, respectively, showing the nonclassical nature of both fields.

Frequency downconversion for a quantum network

By using a parametric downconversion process with a strong signal field injection, we demonstrate coherent frequency downconversion from a pump photon to an idler photon. Contrary to a common misunderstanding, we show that the process can be free of quantum noise. With an interference experiment, we demonstrate that the coherence is preserved in the conversion process. This may lead to a high-fidelity quantum state transfer from a high-frequency photon to a low-frequency photon and connects a missing link in a quantum network. With this scheme of coherent frequency downconversion of photons, we propose a method of single-photon WDM.

Spectral phase conjugation via temporal imaging

We experimentally demonstrate wavelength-preserving spectral phase conjugation for compensating chromatic dispersion and self-phase modulation in optical fibers. Our implementation is based on a temporal imaging scheme that uses time lenses realized by broadband four-wave mixing in silicon waveguides. By constructing a temporal analog of a 4-f imaging system, we compensate for pulse distortions arising from second- and third-order dispersion and self-phase modulation in optical fibers.

Controlling intermodal four-wave mixing from the design of microstructured optical fibers

Intermodal four-wave mixing (FWM) in microstructured optical fibers (MOF) is studied theoretically and experimentally. The dependance of FWM frequency detuning on the geometrical parameters of the fiber, namely the pitch, the core width and the air-filling fraction is derived. We propose to use the results of this investigation to control the position of the Stokes and anti-Stokes waves directly from the fiber transverse structure drawing without the need for time-consuming simulations as in usual design procedures. Stokes sideband can then be freely tuned within the S-, L-, and C- bands with great potential for infrared applications.

Polarization-independent amplification and frequency conversion in strongly-birefringent fibers

The inverse modulation interaction is a degenerate four-wave mixing process in which two strong pumps drive a weak signal, whose frequency is the average of the pump frequencies. Theoretical analyses and numerical simulations of this process are made for wave frequencies that are near the zero-dispersion frequency of a fiber, in which case dispersion is unimportant, and wave frequencies that are far from the zero-dispersion frequency, in which case dispersion is important. The results show that the inverse modulation interaction in a strongly-birefringent fiber amplifies a linearly-polarized signal by an amount that depends on its phase angle, but not its polarization angle. Phase conjugation and Bragg scattering are nondegenerate four-wave mixing processes in which two strong pumps drive a weak signal and a weak idler. Studies show that phase conjugation and Bragg scattering in strongly-birefringent fibers produce polarization-independent phase-insensitive amplification and frequency conversion, respectively.