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Josephson junction cavity systems as cousins of the quantum optical micromaser

Simon Dambach, Andrew D. Armour, Björn Kubala, Joachim Ankerhold

Published Aug 7, 2019• 3 citations
Publisher

Abstract

Abstract We explore the similarities and differences between simple theoretical models developed to describe the quantum optical micromaser and Josephson-photonics devices. Whilst the micromaser has long been recognised as an important model for the dynamics of open quantum systems far from equilibrium, so-called Josephson-photonics devices are a recently developed form of superconducting quantum circuit in which the quantum transport of charges through a voltage-biased Josephson junction drives the production of photons in a microwave resonator.

DOI
10.18725/oparu-46257

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Josephson cascade micromaser

Noriyuki Hatakenaka, Susumu Kurihara

The possibility of maser action using a current-biased mesoscopic Josephson junction in a high-Q microcavity is discussed. A mesoscopic Josephson junction behaves like an artificial atom as far as the interaction with the photon field is concerned. Under a certain bias current, the Josephson ``atom'' is resonantly excited or pumped by quantum-mechanical fluctuations of the Josephson phase, i.e., macroscopic resonant tunneling. When the pumping overcomes the loss of photons from the cavity, maser action is possible. Quantum statistical properties of photons are also investigated numerically, taking into acount the microcavity effect on the basis of a Jaynes-Cummings model with pumping and cavity damping. We found that a mesoscopic Josephson junction within the high-Q microcavity acts as a thresholdless maser with sub-Poissonian photon statstics. \textcopyright{} 1996 The American Physical Society.

Physical Review A•Aug 1, 1996•16 citations
Abstract We explore the similarities and differences between simple theoretical models developed to describe the quantum optical micromaser and Josephson-photonics devices. Whilst the micromaser has long been recognised as an important model for the dynamics of open quantum systems far from equilibrium, so-called Josephson-photonics devices are a recently developed form of superconducting quantum circuit in which the quantum transport of charges through a voltage-biased Josephson junction drives the production of photons in a microwave resonator.
Abstract We explore the similarities and differences between simple theoretical models developed to describe the quantum optical micromaser and Josephson-photonics devices. Whilst the micromaser has long been recognised as an important model for the dynamics of open quantum systems far from equilibrium, so-called Josephson-photonics devices are a recently developed form of superconducting quantum circuit in which the quantum transport of charges through a voltage-biased Josephson junction drives the production of photons in a microwave resonator.
When connecting a voltage-biased Josephson junction in series to several microwave cavities, a Cooper-pair current across the junction gives rise to a continuous emission of strongly correlated photons into the cavity modes. Tuning the bias voltage to the resonance where a single Cooper pair provides the energy to create an additional photon in each of the cavities, we demonstrate the entangling nature of these creation processes by simple witnesses in terms of experimentally accessible observables. To characterize the entanglement properties of the such created quantum states of light to the fullest possible extent, we then proceed to more elaborate entanglement criteria based on the knowledge of the full density matrix and provide a detailed study of bi- and multipartite entanglement. In particular, we illustrate how due to the relatively simple design of these circuits changes of experimental parameters allow one to access a wide variety of entangled states differing, e.g., in the number of entangled parties or the dimension of state space. Such devices, besides their promising potential to act as a highly versatile source of entangled quantum microwaves, may thus represent an excellent natural testbed for classification and quantification schemes developed in quantum information theory.
Abstract When connecting a voltage-biased Josephson junction in series to several microwave cavities, a Cooper-pair current across the junction gives rise to a continuous emission of strongly correlated photons into the cavity modes. Tuning the bias voltage to the resonance where a single Cooper pair provides the energy to create an additional photon in each of the cavities, we demonstrate the entangling nature of these creation processes by simple witnesses in terms of experimentally accessible observables. To characterize the entanglement properties of the such created quantum states of light to the fullest possible extent, we then proceed to more elaborate entanglement criteria based on the knowledge of the full density matrix and provide a detailed study of bi- and multipartite entanglement. In particular, we illustrate how due to the relatively simple design of these circuits changes of experimental parameters allow one to access a wide variety of entangled states differing, e.g., in the number of entangled parties or the dimension of state space. Such devices, besides their promising potential to act as a highly versatile source of entangled quantum microwaves, may thus represent an excellent natural testbed for classification and quantification schemes developed in quantum information theory.
At its heart, a Josephson-photonics device combines macroscopic superconducting electronics and microscopic quantum optics. It consists of a dc-voltage biased Josephson junction that is connected in series to one or a few microwave cavities. Cooper pairs can tunnel incoherently across the junction by depositing their energy 2eVdc in the microwave cavities, creating photonic excitations in them. Many parameters, such as the eigenfrequencies ∝ (LC)^(−1/2) or zero-point fluctuations ∝ (L/C)^(1/4) of the microwave cavities, can be experimentally designed; other parameters, such as the strength of the Josephson nonlinearity and the dc voltage are easily modified in situ. In this way, Josephson-photonics devices constitute a versatile source of microwave photons with a wide variety of features extending from the classical to the deep quantum regime. To make them of use for quantum technological applications that rely on a well-defined phase of the microwave light, a crucial drawback must be overcome. The dc voltage does not provide a stable reference phase to Josephson-photonics devices, as it is subject to experimental noise, such that all phase information is lost. In this thesis, we develop the field of Josephson photonics in two directions: As first main result, we resolve the issue of phase instability in Josephson photonics. The phase can be stabilized either by injection locking to a small external signal with a stable and well-defined reference phase or by mutual synchronization to a second device. An alternative approach mitigates the issue for some use cases by optimizing an ansatz to reconstruct the undiffused stationary quantum state from experiments with phase diffusion. Secondly, we show how Josephson-photonics devices can be used for the challenging task of reliably detecting single itinerant microwave photons. The “Inelastic Cooper Pair Tunneling Photon Multiplier” exploits a resonance condition, where the energy provided by the dc voltage enables a multiplication process from one incoming to n outgoing photons. This process can be staged to reach a large number of outgoing photons. Here, we model itinerant Gaussian single-photon pulses of length T with Mølmer’s approach. Further, we define a detection scheme based on heterodyne quadrature measurement of the output signal. Most importantly, we show that realistic devices can achieve a detection efficiency of 84.5% with a small dark-count rate of 10^(−3)/T, promising to outperform competing schemes.
Abstract We explore the dissipative dynamics of nonlinearly driven oscillator systems tuned to resonances where multiple excitations are generated. Such systems are readily realised in circuit QED systems combining Josephson junctions with a microwave cavity and a drive achieved either through flux or voltage bias. For resonances involving three or more photons the system undergoes a sequence of two closely spaced dynamical transitions (the first one discontinuous and the second continuous) as the driving is increased leading to steady states that form complex periodic structures in phase space. In the vicinity of the transitions the system displays interesting bistable behaviour: we find that coherent effects can lead to surprising oscillations in the weight of the different dynamical states in the steady state of the system with increasing drive. We show that the dynamics is well-described by a simple effective rate model with transitions between states localised at different points in the phase space crystal. The oscillations in the weights of the dynamical states is reflected in corresponding oscillations in a time-scale that describes transitions between the states.
The possibility of maser action using a current-biased mesoscopic Josephson junction in a high-Q microcavity is discussed. A mesoscopic Josephson junction behaves like an artificial atom as far as the interaction with the photon field is concerned. Under a certain bias current, the Josephson ``atom'' is resonantly excited or pumped by quantum-mechanical fluctuations of the Josephson phase, i.e., macroscopic resonant tunneling. When the pumping overcomes the loss of photons from the cavity, maser action is possible. Quantum statistical properties of photons are also investigated numerically, taking into acount the microcavity effect on the basis of a Jaynes-Cummings model with pumping and cavity damping. We found that a mesoscopic Josephson junction within the high-Q microcavity acts as a thresholdless maser with sub-Poissonian photon statstics. \textcopyright{} 1996 The American Physical Society.