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Physical Review Letters

Microwave Cooling of Josephson Plasma Oscillations

Jan Hammer, M. Aprili, Ivana Petković

Published Jun 29, 2011• 7 citations
Publisher

Abstract

An extended Josephson junction can be described as a microwave cavity coupled to a Josephson oscillator. This is formally equivalent to a Fabry-Perot cavity with a freely vibrating mirror, where it has been shown that radiation pressure from photons in the cavity can reduce (increase) the vibrations of the mirror, effectively cooling (heating) it. We demonstrate that, similarly, the superconducting phase difference across a Josephson junction-the Josephson phase-can be "cooled" or "heated" by microwave excitation of the junction and that both these effects increase with microwave power.

DOI
10.1103/physrevlett.107.017001

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An extended Josephson junction can be described as a microwave cavity coupled to a Josephson oscillator. This is formally equivalent to a Fabry-Perot cavity with a freely vibrating mirror, where it has been shown that radiation pressure from photons in the cavity can reduce (increase) the vibrations of the mirror, effectively cooling (heating) it. We demonstrate that, similarly, the superconducting phase difference across a Josephson junction-the Josephson phase-can be "cooled" or "heated" by microwave excitation of the junction and that both these effects increase with microwave power.
An extended Josephson junction intrinsically couples the superconducting current to the microwave cavity in the insulating barrier. We demonstrate that this coupling produces sidebands in the microwave cavity resonances of the junction. By measuring the switching current distribution, we show that microwave radiation at sidebands brings the Josephson phase out of equilibrium. In particular, the effective phase temperature is reduced or enhanced through anti-Stokes and Stokes scattering, respectively. Phase cooling and heating both increase with microwave power.
An extended Josephson junction consists of two superconducting electrodes separated by an insulator and is therefore also a microwave cavity. The superconducting phase difference across the junction determines the amplitude as well as the spatial distribution of the supercurrent. Both external magnetic fields and resonant intracavity fields produce a spatial modification of the superconducting phase along the junction. The interplay between these two effects leads to interference in the critical current of the junction and allows us to continuously tune the coupling strength between the first cavity mode and the Josephson phase from 1 to $\ensuremath{-}0.68$. This enables static and dynamic control of the junction in the ultrastrong-coupling regime.
A high temperature superconducting YBa2Cu3Oy array of five Josephson junctions designed with additional coupling lines has been developed to demonstrate the effects of frequency locking and impedance matching for applications such as oscillators, mixers, and detectors. The Josephson self-radiation power was directly detected by a superheterodyne receiver, and Shapiro steps were also measured. The Josephson self-radiation properties reveal good quality of phase locking and microwave coupling with external circuits. The maximum self-radiation power of our array is about 50 pW which is several ten times higher than that of a single Josephson junction, and its peak point exactly satisfies the Josephson current-voltage relation. The Shapiro-step measurements show that the behavior of current-voltage curve depends on the effective inductance of coupling lines which affects the total impedance of Josephson junction array and microwave coupling. The Josephson oscillation frequency was obtained up to about 880 GHz which is 73% of the maximum available frequency calculated from the characteristic voltage of the Josephson junctions. Experimental results show that this type of Josephson junction array can improve the Josephson self-radiation power and increase the maximum detectable frequency.
The possibility of using very-high-Q superconducting microwave cavities to obtain a strong coupling between the electromagnetic field and a Josephson junction has prompted a study of such systems. Expressions have been obtained describing the dc I-V characteristic of a junction biased so that the Josephson radiation frequency is near a resonance of the cavity in which it is located. The rf power coupled into an X-band (10 GHz) TE011 mode cavity from a weakly coupled junction is approximately 3×10−13 I02 Q W, where I0 is the critical current of the junction and Q is the cavity Q. When the coupling between the junction and cavity is large enough, the I-V characteristic becomes multiple valued and the power coupled to the cavity depends on the state of the system. The maximum power which can be coupled to the cavity is approximately 0.58I0Vdc, where Vdc is the voltage required to bias the junction to the resonant frequency of the cavity.
In the late 1960s and early 1970s, the development of mechanical resonators was pushed forward in efforts to record gravitational waves. In order to push down the limit of the smallest detectable force, the radiation circulating in a Fabry-Perot cavity was demonstrated to modify the damping of the cavity end-mirror suspended to act as a mechanical resonator. A few years later, motivated by the study of the internal properties of atoms and ions, the radiation pressure of light was realized as a means to cool atomic motion. In the following years, the ground-state cooling of ion motion was achieved in landmark studies. For mechanical resonators parametrically coupled to Fabry-Perot cavities, it took much longer to reach quantum ground-state cooling, both in the microwave domain, where the original experiments took place, and in the optical domain. Ground-state cooling in both regimes was reached by three groups during the preparation of this thesis and was largely due to advancements in the fabrication methods. \n \nGround-state cooling allows, in principle, the quantum nature of mechanical resonators to be probed and harnessed. Microwave domain devices, which are focused on in this thesis, have the advantage that nonlinear elements (superconducting quantum bits, qubits) are readily available. These elements enable nonclassical state preparation of the qubit and the subsequent transfer to the microwave cavity. The goal is to transfer these quantum states to mechanical resonators. This would allow mechanics to be used as a quantum mechanical memory in quantum information processing thanks to their long lifetimes. \n \nIn this thesis, various aspects of microwave domain circuit optomechanics are studied. The main goal of this thesis is to study how to enhance the coupling between a quantum regime microwave device and a mechanical resonator by using Josephson junction –based qubits. Coherent interaction between a superconducting qubit and a classical driven mechanical field is demonstrated. The analysis presented in this thesis predicts that ground-state cooling and coherent state transfer is possible in the single-phonon regime with transmon-regime qubits. Also, traditional linear optomechanical systems are considered in which the mechanical resonator is coupled to an electrical resonator. Such systems exhibit a rich spectrum of phenomena from which the quantum-limited amplification and multimode effects are considered in this thesis. It is shown that the system operates near quantum-limited amplification, which could be reached if the mechanical resonator was in the ground state.
We shall present our theoretical studies of a Josephson junction of small size in a lossless cavity. When the size of two superconductors are at order of micrometres and the Josephson coupling constant is adjusted to the correct magnitude, the Josephson junction is found to be reduced to a two-level system owing to the finite-size effect and the quenching of the low-lying single-electronic excitations by the superconducting gap. When such a two-level system is placed in a high-quality microwave cavity, the coupling constant with a single photon g may be extremely large, for instance of the order of 108 s−1. On the other hand, the damping rate of the cavity field is much less than g. Therefore, this two-level system may be used to study the quantum nature of photons and to control the dynamics of quantum fields in the framework of the Jayne-Cummings model much more easily.