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arXiv:1611.07484 · Physical review. B./Physical review. B

Creating photon-number squeezed strong microwave fields by a Cooper-pair injection laser

Martin Koppenhöfer, Juha Leppäkangas, Michael Marthaler

Published Apr 24, 2017• 11 citations
arXivHTMLPDF

Abstract

The use of artificial atoms as an active lasing medium opens a way to construct novel sources of nonclassical radiation. An example is the creation of photon-number squeezed light. Here, we present a design of a laser consisting of multiple Cooper-pair transistors coupled to a microwave resonator. Over a broad range of experimentally realizable parameters, this laser creates photon-number squeezed microwave radiation, characterized by a Fano factor $F\ensuremath{\ll}1$, at a very high resonator photon number. We investigate the impact of gate-charge disorder in a Cooper-pair transistor and show that the system can create squeezed strong microwave fields even in the presence of maximum disorder.

DOI
10.1103/physrevb.95.134515

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The use of artificial atoms as an active lasing medium opens a way to construct novel sources of nonclassical radiation. An example is the creation of photon-number squeezed light. Here, we present a design of a laser consisting of multiple Cooper-pair transistors coupled to a microwave resonator. Over a broad range of experimentally realizable parameters, this laser creates photon-number squeezed microwave radiation, characterized by a Fano factor F\ensuremath≪1F\ensuremath{\ll}1F\ensuremath≪1, at a very high resonator photon number. We investigate the impact of gate-charge disorder in a Cooper-pair transistor and show that the system can create squeezed strong microwave fields even in the presence of maximum disorder.
We consider a two-level system with both a transversal and a longitudinal coupling to the electromagnetic field of a resonator. Using a polaron transformation, this Hamiltonian can be mapped onto a Jaynes-Cummings Hamiltonian with generalized field operators acting on the electromagnetic field in the resonator. In contrast to the usual ladder operators aaa and ${a}^{\ifmmode\dagger\else\textdagger\fi{}}$, these operators exhibit a nonmonotonous coupling strength with respect to the number nnn of photons in the resonator. In particular, there are roots of the coupling between qubit and resonator at certain photon numbers n0{n}_{0}n0​. We show that this effect can be exploited to generate photon-number squeezed light, characterized by a Fano factor $F\ensuremath{\ll}1$, with a large number of photons (e.g., of the order of $1\ifmmode\times\else\texttimes\fi{}{10}^{4}$).
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.
A metamaterial formed by superconducting circuits or quantum dots can serve as an active lasing medium when coupled to a microwave resonator. For these artificial atoms, in contrast to real atoms, variations in their parameters cannot be avoided. In this paper, we examine the influence of disorder on such a multiatom lasing setup. We find that the lasing process evolves into a self-organized stationary state that is quite robust against disorder. The reason is that photons created by those atoms which are in or close to resonance with the resonator stimulate the emission also of more detuned atoms. Not only the number of photons grows with the number of atoms but also the width of the resonance as a function of the detuning. Similar properties are found for other types of disorder such as variations in the individual coupling. We present relations on how the allowed disorder scales with the number of atoms and confirm it by a numerical analysis. We also provide estimates for the sample-to-sample variations to be expected for setups with moderate numbers of atoms.
Cavity optomechanics is showing promise for studying quantum mechanics in large systems. However, the smallness of the radiation-pressure coupling is a serious hindrance. Here we show how the charge tuning of the Josephson inductance in a single-Cooper-pair transistor can be exploited to arrange a strong radiation-pressure-type coupling g0{g}_{0}g0​ between mechanical and microwave resonators. In a certain limit of parameters, such a coupling can also be seen as a qubit-mediated coupling of two resonators. We show that this scheme allows reaching extremely high g0{g}_{0}g0​. Contrary to the recent proposals for exploiting the nonlinearity of a large radiation-pressure coupling, the main nonlinearity in this setup originates from a cross-Kerr type of coupling between the resonators, where the cavity refractive index depends on the phonon number. The presence of this coupling will allow accessing the individual phonon numbers via the measurement of the cavity.