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arXiv:2210.15116 · Physical Review Applied

Noise Properties of a Josephson Parametric Oscillator

Gopika Lakshmi Bhai, Hiroto Mukai, Tsuyoshi Yamamoto, Jaw-Shen Tsai

Published Jan 25, 2023• 3 citations
arXivHTMLPDF

Abstract

We perform noise spectroscopy of a Josephson parametric oscillator (JPO) by implementing a microwave homodyne interferometric measurement scheme. We observe the fluctuations in the self-oscillating output field of the JPO for a long 10-s time interval in a single-shot measurement and characterize the phase and amplitude noise. Furthermore, we investigate the effects of the pump strength on the output noise power spectra of the JPO. We find strong fluctuations in the phase with a $1/{f}^{2}$ characteristic in the phase noise power spectrum, which are suppressed by increasing the pump strength.

DOI
10.1103/physrevapplied.19.014065

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Quantum Electronics and Laser Science Conference•May 12, 1991•0 citations
We perform noise spectroscopy of a Josephson parametric oscillator (JPO) by implementing a microwave homodyne interferometric measurement scheme. We observe the fluctuations in the self-oscillating output field of the JPO for a long 10-s time interval in a single-shot measurement and characterize the phase and amplitude noise. Furthermore, we investigate the effects of the pump strength on the output noise power spectra of the JPO. We find strong fluctuations in the phase with a 1/f21/{f}^{2}1/f2 characteristic in the phase noise power spectrum, which are suppressed by increasing the pump strength.
Injection locking is a well-established technique widely used in optics as well as solid-state devices for efficient suppression of noise. We present the spectroscopic characterization of the effect of the injection-locking signal (ILS) in mitigating the phase noise of a Josephson parametric oscillator, whose output oscillating phase undergoes indeterministic switching between the bistable states with symmetry θ→θ+π. With the injection of a weak locking signal, we measure the phase noise power spectral density of the self-sustained oscillator output state for different locking signal strengths. We observed suppression of phase noise by injection locking. As the ILS strength surpasses more than a few photons, the output state stays completely pinned to the locking phase of the ILS, and the random telegraphic noise due to switching of the states is significantly suppressed.
Crossover between thermal and quantum noise in the externally-pumped Josephson-junction parametric amplifiers is theoretically followed. Two different approaches are used for the analysis : i. Josephson junction is replaced with its RSJ model with the equilibrium source of fluctuations; ii. microscopic theory of the tunnel junctions is used, which takes into account not only thermal and quantum but also shot noise. Because of inconvenience of the noise temperature TNfor the amplifier sensitivity characterization in the quantum limit, we express our results in terms of the figure ΘNwhich is essentially the amplifier output noise energy, reduced to its input (in the classical limit,\Theta_{N}=k_{B}T_{N}). For the nondegenerate amplifier, the minimum value of ΘN. equals hω/2 and is due to quantum noise (zero-point oscillations) in the idle-frequency resonator of the amplifier. For the degenerate amplifier, sensitive to only one quadrature component of the input signal, ΘNcan be made much less than the above "quantum limit" even at operation temperatures much higher thanh\omega/k_{B}, if the Josephson junction characteristic frequency ωcis high enough,h\omega_{c}\gsimk_{B}T. Our analysis of the experimental situatlon shows that the values\Theta_{N}<h\omega/2can be achieved using two-dimensional arrays of a large number (N\simeq100) single-tunnel-junction interferometers with low inductances, inductively coupled to a microwave cavity.
Circuit quantum electrodynamics (cQED) is a prominent platform for quantum information processing, in which microwave photons are confined into resonant cavities coupled to superconducting quantum bits (qubits). The large effective dipole moment of the qubit, in combination with the high energy density of the quasi 1-D resonator allow these systems to enter the so-called strong coupling regime. The quantum state of the qubit can then be assessed by probing the frequency of the resonator, protecting the qubit from otherwise losing its energy to the environment. However, eventhough this so-called dispersive readout technique has proven useful, it is often in itself insufficient to render single-shot readout performance | one of the crucial tasks required for realizing a quantum computer. This thesis describes the demonstration of a single-shot readout technique forsuperconducting quantum bits, based on coupling the qubit to a frequency-tunable resonator. The backbone of our device is a 5 GHz quarter-wavelength coplanar waveguide resonator, terminated at one end by a non-linear inductance provided by a superconducting quantum interference device (SQUID). The SQUID acts as a flux-controlled boundary condition, which effectively changes the electrical length of the resonator. This enables the modulation of the resonant frequency by coupling microwave magnetic flux into the SQUID, using an on-chip transmission line. The modulation occurs on a timescale much faster than the photon loss out of the resonator and if the pump strength exceeds a threshold value set by the damping rate of the resonator, an intense photon field will build up inside the resonator | known as "parametric oscillations". By heterodyne detection of the output signal from the Josephson parametric oscillator (JPO), we first extracted two leading nonlinear effects of the system (dominating in different limits of applied magnetic flux). Next, we couple a qubit to the JPO and demonstrate that we can encode its quantum state onto the strong output field of the parametric oscillator (or lack thereof), rendering a signal-to-noise ratio sufficient for single-shot state detection and therefore also obviating a quantum limited parametric amplifier. The thesis also contains results from microscopic studies of the Josephson junctions, which we use to provide the necessary nonlinearities in the above mentioned devices. In particular, we show how the microstructure of the barrier layer and its atomic composition can be used to infer important electrical properties of the junctions. This knowledge allows us to better tailor the properties of Josephson-based devices.
Experimental results are reported on a Josephson parametric upconverting amplifier which is self-pumped via the internal Josephson oscillations derived from a dc bias voltage. A niobium point-contact SQUID is simultaneously coupled to a 115-MHz tank circuit and a 9-GHz cavity. Josephson oscillations at 9 GHz produce parametric upconversion of power in the 115-MHz circuit to sidebands at 9±0.115 GHz with measured power gain of 25. The amplifier noise temperature, referred to the input at 115 MHz, was established to be <15 K by varying the temperature of an input termination from 4.2 to 300 K. This result establishes the behavior of self-pumped SQUID upconverters at microwave frequencies and demonstrates that the achievable noise performance is not greatly in excess of the thermal limit.
We have investigated the performance of a resistive rf SQUID as a 9 GHz parametric amplifier and oscillator. It was coupled to a low impedance microstrip transformer. Stable Josephson oscillations were obtained for βLQ =2eI0ZL/hf <1.1–1.8. Oscillation linewidth (830 kHz) and output power (−74 dBm) were measured. The four-photon internally pumped amplifier produced large single sideband (ssb) noise temperatures, typically around 50 K, due to the broad flanks of the pump. The best performance was achieved in the three- and four-photon externally pumped modes. Both modes gave signal gains of about 10 dB and negligible noise power contributions. A hot/cold measurement on the four-photon amplifier yielded Gdsb =13 dB (dsb=double sideband) and Tdsb =3±4 K over a bandwidth of 310 MHz. For larger values of βLQ , subharmonics 1/2 and 1/3, as well as noninteger ‘‘excitations’’ of the Josephson oscillation, were observed. The subharmonic oscillations were not tunable in frequency with unchanged linewidth. Amplification close to an excitation also produced gain but with ssb noise temperatures of ∼20 K.