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arXiv:1506.05626 · Physical Review B

Time-resolved statistics of nonclassical light in Josephson photonics

Simon Dambach, Björn Kubala, Vera Gramich, Joachim Ankerhold

Published Aug 17, 2015• 42 citations
arXivHTMLPDF

Abstract

The interplay of the tunneling transfer of charges and the emission and absorption of light can be investigated in a setup, where a voltage-biased Josephson junction is connected in series with a microwave cavity. We focus here on the emission processes of photons and analyze the underlying time-dependent statistics using the second-order correlation function ${g}^{(2)}(\ensuremath{\tau})$ and the waiting-time distribution $w(\ensuremath{\tau})$. Both observables highlight the crossover from a coherent light source to a single-photon source. Due to the nonlinearity of the Josephson junction, tunneling Cooper pairs can create a great variety of nonclassical states of light even at weak driving. Analytical results for the weak driving as well as the classical regime are complemented by a numerical treatment for the full nonlinear case. We also address the question of possible relations between ${g}^{(2)}(\ensuremath{\tau})$ and $w(\ensuremath{\tau})$ as well as the specific information which is provided by each of them.

DOI
10.1103/physrevb.92.054508

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The interplay of the tunneling transfer of charges and the emission and absorption of light can be investigated in a setup, where a voltage-biased Josephson junction is connected in series with a microwave cavity. We focus here on the emission processes of photons and analyze the underlying time-dependent statistics using the second-order correlation function g(2)(\ensuremathτ){g}^{(2)}(\ensuremath{\tau})g(2)(\ensuremathτ) and the waiting-time distribution w(\ensuremathτ)w(\ensuremath{\tau})w(\ensuremathτ). Both observables highlight the crossover from a coherent light source to a single-photon source. Due to the nonlinearity of the Josephson junction, tunneling Cooper pairs can create a great variety of nonclassical states of light even at weak driving. Analytical results for the weak driving as well as the classical regime are complemented by a numerical treatment for the full nonlinear case. We also address the question of possible relations between g(2)(\ensuremathτ){g}^{(2)}(\ensuremath{\tau})g(2)(\ensuremathτ) and w(\ensuremathτ)w(\ensuremath{\tau})w(\ensuremathτ) as well as the specific information which is provided by each of them.
The interplay of the tunneling transfer of charges and the emission and absorption of light can be investigated in a set-up, where a voltage-biased Josephson junction is placed in series to a microwave cavity. Here, we concentrate on the emission process and show that due to the inherent nonlinearity of the Josephson junction tunneling Cooper-pairs can create a variety of non-classical states of light. Depending on experimental parameters and tuning the device can be described by effective Hamiltonians, indicating specific photon creation mechanisms which lead to strongly bunched or anti-bunched light emission. We derive explicit analytical expressions for the photon correlation function g(2)(τ=0)g^{(2)}(τ=0)g(2)(τ=0) for these different processes and investigate their full crossover numerically. Photon distribution functions show squeezing and other interesting non-Poissonian behavior.
We analyze the creation and emission of pairs of highly nonclassical microwave photons in a setup where a voltage‐biased Josephson junction is connected in series to two electromagnetic oscillators. Tuning the external voltage such that the Josephson frequency equals the sum of the two mode frequencies, each tunneling Cooper pair creates one additional photon in both of the two oscillators. The time‐resolved statistics of photon emission events from the two oscillators is investigated by means of single‐ and cross‐oscillator variants of the second‐order correlation function and the waiting‐time distribution . They provide insight into the strongly correlated quantum dynamics of the two oscillator subsystems and reveal a rich variety of quantum features of light including strong antibunching and the presence of negative values in the Wigner function.
Weanalyse the full counting statistics (FCS) of photons flowing in and out of a microwave cavity coupled to a voltage-biased Josephson junction. Tunnelling of Cooper pairs generates a coherent flow of photons into the cavity whilst at the same time photons can also leak out incoherently.Weuse a very general unitary transformation method to demonstrate that there is a simple connection between the FCS of the charges and the photons in the long time limit, revealing that all the cumulants of the coherent and the incoherent processes match in that limit.Wealso explore some of the interesting features in the counting statistics of the charges and photons which arise from the strongly nonlinear dynamics of the system. These include very narrow distributions associated with the emergence of coherent transport and regimes where counting of either an odd or an even number of photons leaving the cavity can result in strongly non-classical cat states within the cavity.
Abstract We analyse the full counting statistics (FCS) of photons flowing in and out of a microwave cavity coupled to a voltage-biased Josephson junction. Tunnelling of Cooper pairs generates a coherent flow of photons into the cavity whilst at the same time photons can also leak out incoherently. We use a very general unitary transformation method to demonstrate that there is a simple connection between the FCS of the charges and the photons in the long time limit, revealing that all the cumulants of the coherent and the incoherent processes match in that limit. We also explore some of the interesting features in the counting statistics of the charges and photons which arise from the strongly nonlinear dynamics of the system. These include very narrow distributions associated with the emergence of coherent transport and regimes where counting of either an odd or an even number of photons leaving the cavity can result in strongly non-classical cat states within the cavity.
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.