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arXiv:1510.04168 · Physical Review A

Creation of a squeezed photon distribution using artificial atoms with broken inversion symmetry

Martin Koppenhöfer, Michael Marthaler

Published Feb 22, 2016• 15 citations

Abstract

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 $a$ and ${a}^{\ifmmode\dagger\else\textdagger\fi{}}$, these operators exhibit a nonmonotonous coupling strength with respect to the number $n$ of photons in the resonator. In particular, there are roots of the coupling between qubit and resonator at certain photon numbers ${n}_{0}$. 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 $1\ifmmode\times\else\texttimes\fi{}{10}^{4}$).

DOI: 10.1103/physreva.93.023831

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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

a

and

{a}^{\ifmmode\dagger\else\textdagger\fi{}}

, these operators exhibit a nonmonotonous coupling strength with respect to the number

n

of photons in the resonator. In particular, there are roots of the coupling between qubit and resonator at certain photon numbers

{n}_{0}

. 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}

).

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.

We study the coupled system of the dressed atom and the quantized mode of the electromagnetic field (an open modification of the Jaynes-Cummings model). The mode is initially excited to the coherent quantum state and exhibits Poissonian photon statistics. When the quasienergy levels of the dressed atom cross, the mean number of photons in the mode oscillates at high amplitude. Numerical results show that the photon statistics in the mode regularizes, correlating as the value of falls. Near the local minima of , the statistics can become sub-Poissonian with Fano factor many times smaller than unity.

Quantum-statistical properties such as the photon-number probability distribution and sub-Poissonian distribution are studied by considering the resonant interaction of two radiation fields, one of which is in a squeezed state with a cascade-structure three-level atom. It is noteworthy to emphasize that the direction of squeezing, i.e., the angle \ensuremath{\theta}, and the squeezing parameter r as well as the initial atomic state play important roles in the determination of the nonclassical behavior of the radiation field. At the same time we give a possible explanation for the effect of the ratio of the intensity of the two fields on the quantum-statistical properties.

We introduce a dynamical system that instead of exchanging a single photon as in the atomic system of the usual Jaynes-Cummings model (JCM), it exchanges instead a squeezed coherent photon. Accordingly, the creation and annihilation photon operators in the JCM are replaced by the creation and annihilation operators of squeezed coherent states, respectively. This transformation generates a photon Hamiltonian that modifies the JCM that includes terms usually omitted in the JCM when making the rotating-wave approximation and, in addition, the transformation introduces atom exchange terms absent in the JCM.

If a two-level atom is in the two-photon resonance with a quantized mode and simultaneously inter-acts with a quasi-resonance classical field, then a photon exchange is observed in this system between the quantized and classical modes. It is demonstrated that such a physical system can serve as a source of squeezed radiation in the quantized mode. The squeezing can be arbitrarily close to unity, while the radiation amplitude can be relatively large. A situation is discussed when N atoms are in the two-photon resonance with a quantized mode and simultaneously interact with a classical field. The phenomenon of exponential superradiation is described when the number of photons in the quantized mode exponentially depends on the number N of atoms.