Traveling-wave Parametric Amplifier Research Articles

Squeezing and quantum state engineering with Josephson travelling wave amplifiers

We develop a quantum theory describing the input–output properties of Josephson traveling wave parametric amplifiers. This allows us to show how such a device can be used as a source of nonclassical radiation, and how dispersion engineering can be used to tailor gain profiles and squeezing spectra with attractive properties, ranging from genuinely broadband spectra to “squeezing combs” consisting of a number of discrete entangled quasimodes. The device’s output field can furthermore be used to generate a multi-mode squeezed bath—a powerful resource for dissipative quantum state preparation. In particular, we show how it can be used to generate continuous variable cluster states that are universal for measurement based quantum computing. The favorable scaling properties of the preparation scheme makes this a promising path towards continuous variable quantum computing in the microwave regime.

Topological Quantum Fluctuations and Traveling Wave Amplifiers

It is now well-established that photonic systems can exhibit topological energy bands; similar to their electronic counterparts, this leads to the formation of chiral edge modes which can be used to transmit light in a manner that is protected against back-scattering. While it is understood how classical signals can propagate under these conditions, it is an outstanding important question how the quantum vacuum fluctuations of the electromagnetic field get modified in the presence of a topological band structure. We address this challenge by exploring a setting where a non-zero topological invariant guarantees the presence of a parametrically-unstable chiral edge mode in a system with boundaries, even though there are no bulk-mode instabilities. We show that one can exploit this to realize a topologically protected, quantum-limited travelling-wave parametric amplifier. The device is naturally protected both against internal losses and back-scattering; the latter feature is in stark contrast to standard travelling wave amplifiers. This adds a new example to the list of potential quantum devices that profit from topological transport.

Implementation of Traveling Odd Schrödinger Cat States in Circuit-QED

We propose a realistic scheme of generating a traveling odd Schrödinger cat state and a generalized entangled coherent state in circuit quantum electrodynamics (circuit-QED). A squeezed vacuum state is used as the initial resource of nonclassical states, which can be created through a Josephson traveling-wave parametric amplifier, and travels through a transmission line. Because a single-photon subtraction from the squeezed vacuum gives an odd Schrödinger cat state with very high fidelity, we consider a specific circuit-QED setup consisting of the Josephson amplifier creating the traveling resource in a line, a beam-splitter coupling two transmission lines, and a single photon detector located at the end of the other line. When a single microwave photon is detected by measuring the excited state of a superconducting qubit in the detector, a heralded cat state is generated with high fidelity in the opposite line. For example, we show that the high fidelity of the outcome with the ideal cat state can be achieved with appropriate squeezing parameters theoretically. As its extended setup, we suggest that generalized entangled coherent states can be also built probabilistically and that they are useful for microwave quantum information processing for error-correctable qudits in circuit-QED.

Parametric Amplification in a Superconducting Microstrip Transmission Line

Broadband parametric amplifiers (PAs), which utilize the nonlinear kinetic inductance of superconducting transmission lines, provide new access to ultimate sensing capability for radio astronomical observation and microwave quantum electronics. In this paper, the parametric amplification is investigated with a time-domain numerical method. The results present direct images of the traveling waves, which clarify the distinctively different features of the parametric gain in uniform and impedance-perturbed nonlinear transmission lines. The results indicate that the traveling-wave PAs (TWPAs) are susceptible to impedance mismatching because of the lack of isolation between the input and the output ports. In the experimental part of this paper, we tested, for the first time, microstrip TWPAs based on NbTiN. A parametric gain was observed at liquid helium temperature.

Resonance Fluorescence from an Artificial Atom in Squeezed Vacuum

We present an experimental realization of resonance fluorescence in squeezed vacuum. We strongly couple microwave-frequency squeezed light to a superconducting artificial atom and detect the resulting fluorescence with high resolution enabled by a broadband traveling-wave parametric amplifier. We investigate the fluorescence spectra in the weak and strong driving regimes, observing up to 3.1 dB of reduction of the fluorescence linewidth below the ordinary vacuum level and a dramatic dependence of the Mollow triplet spectrum on the relative phase of the driving and squeezed vacuum fields. Our results are in excellent agreement with predictions for spectra produced by a two-level atom in squeezed vacuum [Phys. Rev. Lett. \textbf{58}, 2539-2542 (1987)], demonstrating that resonance fluorescence offers a resource-efficient means to characterize squeezing in cryogenic environments.

Superconducting microwave parametric amplifier based on a quasi-fractal slow propagation line

Quantum limited amplifiers are sought after for a wide range of applications within quantum technologies and sensing. One promising candidate is the travelling wave parametric amplifier which exploits the non-linear kinetic inductance of a superconducting transmission line. This type of microwave amplifier promises to deliver a high gain, a quantum limited noise performance over several GHz bandwidth, and a high dynamic range. However, practical realizations of this type of device have so far been limited by fabrication defects, since the length of the superconducting transmission line required for achieving substantial parametric gain is on the order of ∼1 m. Here, we report on a design for a microwave traveling wave amplifier based on a slow propagation line comprising a central strip with high kinetic inductance and quasi-fractal line-to-ground capacitors. Due to an enhanced per unit length inductance (73 nH cm−1) and capacitance (15 pF cm−1), the line has a microwave propagation velocity as low as 9.8 × 108 cm s−1. This translates into parametric gain up to 0.5 dB cm−1 and a total gain of 6 dB for just a ∼10 cm long transmission line. Moreover, the flexibility of the presented design allows balancing the line inductance and capacitance in order to keep the characteristic impedance close to 50 Ω and to suppress standing waves, both factors being essential in order to implement a practical parametric amplifier in the microwave domain.

Higher-order nonlinear effects in a Josephson parametric amplifier

Nonlinearity of the current-phase relationship of a Josephson junction is the key resource for a Josephson parametric amplifier (JPA) as well as for a Josephson traveling-wave parametric amplifier, the only devices in which the quantum limit for added noise has so far been approached at microwave frequencies. A standard approach to describe JPA takes into account only the lowest order (cubic) nonlinearity resulting in a Duffing-like oscillator equation of motion or in a Kerr-type nonlinearity term in the Hamiltonian. In this paper we derive the quantum expression for the gain of JPA including all orders of the Josephson junction nonlinearity in the linear response regime. We then analyze gain saturation effect for stronger signals within a semiclassical approach. Our results reveal nonlinear effects of higher orders and their implications for operation of a JPA.

Traveling-Wave Parametric Amplifier Based on a Chain of Coupled Asymmetric SQUIDs

A traveling wave parametric amplifier (TWPA) composed of a transmission line made up of a chain of coupled asymmetric superconducting quantum interference devices (SQUIDs) is proposed. The unique nature of this transmission line is that its nonlinearity can be tuned with an external magnetic flux and can even change sign. This feature of the transmission line can be used to perform phase matching in a degenerate four-wave mixing process which can be utilized for parametric amplification of a weak signal in the presence of a strong pump. Numerical simulations of the TWPA design have shown that with tuning, phase matching can be achieved and an exponential gain as a function of the transmission line length can be realized. The flexibility of the proposed design can realize: compact TWPAs with less than 211 unit cells, signal gains greater than 20 dB, 3 dB bandwidth greater than 5.4 GHz, and saturation powers up to -98 dBm. This amplifier design is well suited for multiplexed readout of quantum circuits or astronomical detectors in a compact configuration which can foster on-chip implementations.

Traveling wave parametric amplifier with Josephson junctions using minimal resonator phase matching

Josephson parametric amplifiers have become a critical tool in superconducting device physics due to their high gain and quantum-limited noise. Traveling wave parametric amplifiers (TWPAs) promise similar noise performance, while allowing for significant increases in both bandwidth and dynamic range. We present a TWPA device based on an LC-ladder transmission line of Josephson junctions and parallel plate capacitors using low-loss amorphous silicon dielectric. Crucially, we have inserted λ/4 resonators at regular intervals along the transmission line in order to maintain the phase matching condition between pump, signal, and idler and increase gain. We achieve an average gain of 12 dB across a 4 GHz span, along with an average saturation power of −92 dBm with noise approaching the quantum limit.

Resonant phase matching of Josephson junction traveling wave parametric amplifiers.

We propose a technique to overcome phase mismatch in Josephson-junction traveling wave parametric amplifiers in order to achieve high gain over a broad bandwidth. Using "resonant phase matching," we design a compact superconducting device consisting of a transmission line with subwavelength resonant inclusions that simultaneously achieves a gain of 20 dB, an instantaneous bandwidth of 3 GHz, and a saturation power of -98 dBm. Such an amplifier is well suited to cryogenic broadband microwave measurements such as the multiplexed readout of quantum coherent circuits based on superconducting, semiconducting, or nanomechanical elements, as well as traditional astronomical detectors.

Bright squeezed-vacuum source with 1.1 spatial mode.

Bright squeezed vacuum, a macroscopic nonclassical state of light, can be obtained at the output of a strongly pumped nonseeded traveling-wave optical parametric amplifier (OPA). By constructing the OPA of two consecutive crystals separated by a large distance, we make the squeezed vacuum spatially single-mode without a significant decrease in the brightness or squeezing.

Simulation and Analysis of Superconducting Traveling-Wave Parametric Amplifiers

Superconducting parametric amplifiers have great promise for quantum-limited readout of superconducting qubits and detectors. Until recently, most superconducting parametric amplifiers had been based on resonant structures, limiting their bandwidth and dynamic range. Broadband traveling-wave parametric amplifiers based both on the nonlinear kinetic inductance of superconducting thin films and on Josephson junctions are in development. By modifying the dispersion property of the amplifier circuit, referred to as dispersion engineering, the gain can be greatly enhanced and the size can be reduced. We present two theoretical frameworks for analyzing and understanding such parametric amplifiers: 1) generalized coupled-mode equations and 2) a finite difference time domain (FDTD) model combined with a small signal analysis. We show how these analytical and numerical tools may be used to understand device performance.

Fundamental eigenmode of traveling-wave phase-sensitive optical parametric amplifier: experimental generation and verification

We investigate experimentally the eigenmodes of a Gaussian-beam-pumped traveling-wave phase-sensitive optical parametric amplifier (PSA). By varying the waist of an input LG(00) signal mode, we show that PSA performance improves with increasing spatial overlap between the input and the theoretically predicted fundamental eigenmode. For optimum waist, we report amplification and deamplification markedly higher than those observed for the traditional case of signal waist=√2× (pump waist). Lastly, we demonstrate the generation and verification of the PSA fundamental eigenmode.

Optimization of gain in traveling-wave optical parametric amplifiers by tuning the offset between pump- and signal-waist locations

We present experimental demonstration and modeling of the optimization of a phase-sensitive optical parametric amplifier by tuning the relative position between the pump and signal beam waists along the propagation direction. At the optimum position, the pump beam focuses after the signal beam, and this departure from colocated waists increases with increasing pump power. Such optimization leads to more than 3dB improvement in the measured deamplification response of the amplifier.

Quantum properties of a spatially-broadband traveling-wave phase-sensitive optical parametric amplifier

We present the quantum theory of a spatially-multimode traveling-wave phase-sensitive optical parametric amplifier (OPA) pumped by a beam with arbitrary spatial profile. By using Green's functions of the classical OPA, we derive the normally-ordered quadrature correlators at the OPA output, which provide complete quantum description of the phase-sensitive OPA and enable determination of its independently-squeezed eigenmodes. Two analytically treatable examples of plane-wave pump and infinite spatial bandwidth of the crystal are discussed in detail.

Numerical simulation of spatial fluctuations in parametric image amplification

We study the properties of the spatial fluctuations in the far-field parametric fluorescence output of a type 1 degenerate traveling-wave parametric amplifier. Results of a semi-classical simulation are compared with experiments in a LBO crystal. This simulation is then used to predict amplified images of a continuous background, in a phase-sensitive as well as in a phase-insensitive configuration.

Sum-frequency generation of femtosecond pulses in CsLiB_6O_10 down to 175 nm

Using a 150-mum-thick CsLiB(6)O(10) crystal, we produced 100-fs, >200-nJ light pulses tunable between 175 and 180 nm by sum-frequency generation at a 1-kHz repetition rate with an all-solid-state laser system mixing the fourth harmonic of a femtosecond Ti:sapphire regenerative amplifier and the idler pulse from a traveling-wave optical parametric amplifier.

Generation of widely tunable harmonic pulses in the UV and VUV from a NIR optical parametric amplifier

We demonstrate the generation of tunable high-order harmonics from the interaction of the signal output of a near-infrared (NIR) traveling-wave optical parametric amplifier (OPA) with the xenon atoms of a pulsed gas jet. By tuning the OPA between 1200 and 1550 nm, we generate widely tunable pulses of ultraviolet radiation up to the ninth harmonic order, around 150 nm. The possibility to cover the VUV region thanks to the full overlap of the tunability ranges of different harmonic orders below 220 nm is also proved.

Laser-diode-seeded single and double stage femtosecond optical parametric amplification in the mid-infrared

Tunable mid-infrared pulses are generated with a MgO:LiNbO3-based traveling-wave optical parametric amplifier in single and double stage operation regime pumped by a 1-kHz Ti:sapphire regenerative amplifier system. For the first time to our knowledge a pulsed laser diode is successfully used in the femtosecond regime as a compact seed source at the signal wavelength where the tunability of the generated idler pulses can be realized by tuning the seed wavelength. Almost transform limited mid-infrared pulses as short as 130 and 160 fs with pulse energies as high as 5 and 15 μJ are produced near 3.5 μm by the single and double stage scheme, respectively. The pulse to pulse fluctuations in both cases do not exceed 2% which corresponds to the stability of the pump source.

Quantum fluctuations in traveling-wave amplification of optical images

We investigate amplification of optical images by means of a traveling-wave optical parametric amplifier. As shown recently for a cavity-based geometry, such a scheme can amplify images without deteriorating their signal-to-noise ratio thus working as a noiseless amplifier. Here we consider a configuration without cavity, which is more realistic for a possible experimental realization. We study in detail the quantum fluctuations of the amplifier and formulate criteria for its noiseless performance. We investigate physical features of noiseless amplification, which take place for both traveling-wave and ring-cavity configurations. We demonstrate how the optimum phase matching of a phase-sensitive wave front of an image (by means of a thin lens or a small displacement of the crystal) can improve the noise performance of the amplifier and bring it to the ultimate value achievable under given physical conditions. We discuss the possibility of using detectors with the area much smaller than the area of the input image elements. We compare our results with those obtained for the ring-cavity configuration.