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arXiv:2301.06791 · Applied Physics Letters

Mitigation of noise in Josephson parametric oscillator by injection locking

Gopika Lakshmi Bhai, Hiroto Mukai, Jaw-Shen Tsai

Published Jan 30, 2023• 3 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1063/5.0134702

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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.
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 can stabilize a source of radiation, leading to an efficient suppression of noise-induced spectral broadening and therefore, to a narrow spectrum. The technique is well established in laser physics, where a phenomenological description due to Adler is usually sufficient. Recently, locking experiments were performed in Josephson photonics devices, where microwave radiation is created by inelastic Cooper pair tunneling across a dc-biased Josephson junction connected in-series with a microwave resonator. An in-depth theory of locking for such devices, accounting for the Josephson nonlinearity and the specific engineered environments, is lacking. Here, we study injection locking in a typical Josephson photonics device where the environment consists of a single mode cavity, operated in the classical regime. We show that an in-series resistance, however small, is an important ingredient in describing self-sustained Josephson oscillations and enables the locking region. We derive a dynamical equation describing locking, similar to an Adler equation, from the specific circuit equations. The effect of noise on the locked Josephson phase is described in terms of phase slips in a modified washboard potential. For weak noise, the spectral broadening is reduced exponentially with the injection signal. When this signal is provided from a second Josephson device, the two devices synchronize. In the linearized limit, we recover the Kuramoto model of synchronized oscillators. The picture of classical phase slips established here suggests a natural extension towards a theory of locking in the quantum regime.
Bright sources of quantum microwave light are an important building block for various quantum technological applications. Josephson junctions coupled to microwave cavities are a particularly versatile and simple source for microwaves with quantum characteristics, such as different types of squeezing. Due to the inherent nonlinearity of the system, a pure dc-voltage bias can lead to the emission of correlated pairs of photons into a stripline resonator. However, a drawback of this method is that it suffers from bias voltage noise, which disturbs the phase of the junction and consequently destroys the coherence of the photons, severely limiting its applications. Here we describe how adding a small ac reference signal either to the dc bias or directly into the cavity can stabilize the system and counteract the sensitivity to noise. We first consider the injection locking of a single-mode device before turning to the more technologically relevant locking of two-mode squeezed states, where phase locking preserves the entanglement between photons. Finally, we describe locking by directly injecting a microwave into the cavity, which breaks the symmetry of the squeezing ellipse. In all cases, locking can mitigate the effects of voltage noise and enable the use of squeezed states in quantum technological applications.
Experimental investigations illustrating the intensity noise properties of injection-locked solid-state lasers were performed. The measured results are predicted by a quantum mechanical model. The theory describes the intensity noise transfer to the slave laser’s output for large modulation signals as well as for signals at the quantum noise level. Different frequency regions in the intensity noise spectrum are identified and it is shown that there exist different minimum noise levels in these regions. Under appropriate conditions, injection-locked lasers can generate non-classical light.
Injection locking replicates the frequency and phase of a driven oscillator in a target oscillator, with applications in electronic, mechanical, and optical systems, and lately in mesoscopic circuits. The technique requires the driven oscillator to be almost resonant with the target oscillator. This study uses a superconducting circuit to demonstrate injection locking in a well-controlled parametric microwave oscillator. The authors furthermore present another technique, $p\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}m\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}c$ $l\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}c\phantom{\rule{0}{0ex}}k\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}g$, that removes the constraint on detuning between the oscillators. This should impact any device that should not or cannot be close to resonant driving, as in quantum information processing.
Stability of Josephson junction clock sources can be a limiting factor in the operation of RSFQ digital and mixed signal circuits. We have developed techniques for the characterization of the short-term stability, i.e., the jitter, of Josephson junction clock sources, and in this paper we present measurements of the jitter for a long Josephson junction soliton oscillator clock. The output frequency of the soliton oscillator was prescaled by using a chain of T flip-flops and using a current bias feedback the oscillator was phase locked to a stable room temperature RP source. Phase noise spectra of the clock signal were measured at the successive stages of the T flip-flop chain and interpreted to infer the cycle-to-cycle jitter of the soliton oscillator. The jitter at the output of the soliton oscillator was measured to be 60 fs at a frequency of 26 GHz, or 0.16% of the period of the clock.