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arXiv:1604.03830 · Physical review. B./Physical review. B

Electron-photon interaction in a quantum point contact coupled to a microwave resonator

Udson C. Mendes, Christophe Mora

Published Jun 29, 2016• 14 citations
arXivHTMLPDF

Abstract

We study a single-mode cavity weakly coupled to a voltage-biased quantum point contact. In a perturbative analysis, the lowest order predicts a thermal state for the cavity photons, driven by the emission noise of the conductor. The cavity is thus emptied as all transmission probabilities of the quantum point contact approach one or zero. Two-photon processes are identified at higher coupling, and pair absorption dominates over pair emission for all bias voltages. As a result, the number of cavity photons, the cavity damping rate, and the second-order coherence ${g}^{(2)}$ are all reduced and exhibit less bunching than the thermal state. These results are obtained with a Keldysh path-integral formulation and reproduced with rate equations. They can be seen as a backaction of the cavity measuring the electronic noise. Extending the standard $P(E)$ theory to a steady-state situation, we compute the modified noise properties of the conductor and find quantitative agreement with the perturbative calculation.

DOI
10.1103/physrevb.93.235450

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We study a single-mode cavity weakly coupled to a voltage-biased quantum point contact. In a perturbative analysis, the lowest order predicts a thermal state for the cavity photons, driven by the emission noise of the conductor. The cavity is thus emptied as all transmission probabilities of the quantum point contact approach one or zero. Two-photon processes are identified at higher coupling, and pair absorption dominates over pair emission for all bias voltages. As a result, the number of cavity photons, the cavity damping rate, and the second-order coherence g(2){g}^{(2)}g(2) are all reduced and exhibit less bunching than the thermal state. These results are obtained with a Keldysh path-integral formulation and reproduced with rate equations. They can be seen as a backaction of the cavity measuring the electronic noise. Extending the standard P(E)P(E)P(E) theory to a steady-state situation, we compute the modified noise properties of the conductor and find quantitative agreement with the perturbative calculation.
Shot noise of electrons that are transmitted with probability TTT through a quantum point contact (biased at a voltage V0{V}_{0}V0​) leads to a fluctuating current that in turn emits radiation in the microwave regime. By calculating the Fano factor FFF for the case where only a single channel contributes to the transport, it has been shown that the radiation produced at finite frequency ${\ensuremath{\omega}}_{0}$ close to $e{V}_{0}/\ensuremath{\hbar}$ and at low temperatures is nonclassical with sub-Poissonian statistics (F<1F<1F<1). The origin of this effect is the fermionic nature of the electrons producing the radiation, which reduces the probability of simultaneous emission of two or more photons. However, the Fano factor, being a time-averaged quantity, offers only limited information about the system. Here, we calculate the second-order coherence ${g}^{(2)}(\ensuremath{\tau})$ for this source of radiation. We show that due to the interference of two contributions, two photon processes (leading to bunching) are completely absent at zero temperature for T=50T=50\phantom{\rule{0.16em}{0ex}}%T=50. At low temperatures, we find a competition of the contribution due to Gaussian current-current fluctuations (leading to bunching) with the one due to non-Gaussian fluctuations (leading to antibunching). At slightly elevated temperatures, the non-Gaussian contribution becomes suppressed, whereas the Gaussian contributions remain largely independent of temperature. We show that the competition of the two contributions leads to a nonmonotonic behavior of the second-order coherence as a function of time. As a result, ${g}^{(2)}(\ensuremath{\tau})$ obtains a minimal value for times ${\ensuremath{\tau}}^{*}\ensuremath{\simeq}{\ensuremath{\omega}}_{0}^{\ensuremath{-}1}$. Close to this time, the second-order coherence remains below 1 at temperatures where the Fano factor is already above 1. We identify realistic experimental parameters that can be used to test the sub-Poissonian nature of the radiation.
Hybrid architectures integrating mesoscopic electronic conductors with resonant microwave cavities have a great potential for investigating unexplored regimes of electron–photon coupling. In this context, producing nonclassical squeezed light is a key step towards quantum communication with scalable solid-state devices. Here we show that parametric driving of the electronic conductor induces a squeezed steady state in the cavity. We find that squeezing properties of the cavity are essentially determined by the electronic noise correlators of the quantum conductor. In the case of a tunnel junction, we predict that squeezing is optimized by applying a time-periodic series of quantized δ —peaks in the bias voltage. For an asymmetric quantum dot, we show that a sharp Leviton pulse is able to achieve perfect cavity squeezing.
We use a superconducting microresonator as a cavity to sense absorption of microwaves by a superconducting quantum point contact defined by surface gates over a proximitized two-dimensional electron gas. Renormalization of the cavity frequency with phase difference across the point contact is consistent with coupling to Andreev bound states. Near \ensuremath{\pi} phase difference, we observe random fluctuations in absorption with gate voltage, related to quantum interference-induced modulations in the electron transmission. Close to pinch-off, we identify features consistent with the presence of a single Andreev bound state and describe the Andreev-cavity interaction using a Jaynes-Cummings model. By fitting the weak Andreev-cavity coupling, we extract \ensuremath{\sim}GHz decoherence consistent with charge noise and the transmission dispersion associated with a localized state.
Self-sustained oscillators play a central role in the stabilization and synchronization of complex dynamical systems. A number of different physical systems are currently being investigated to clarify the importance of such active components in the quantum realm. Here we explore the properties of a driven dissipative electron-photon hybrid system based on superconducting microwave resonators coupled resonantly to a voltage-biased double quantum dot (DQD). First, we establish a Hopf bifurcation at a critical value of the electron-photon coupling, beyond which an effective negative friction sustains steady limit-cycle oscillations of individual resonators. Second, we show that two such limit-cycle resonators coupled via the same voltage-biased DQD synchronize for small enough frequency detuning. A nonlinear photon Keldysh action is derived by perturbation theory in the effective circuit fine-structure constant, and the limit-cycle dynamics is analyzed in terms of resulting saddle-point, and Fokker-Planck equations. In the Markovian limit of infinite bias voltage, these results are shown to agree well with the solution of a corresponding Lindblad master equation for the DQD resonator system.
We give a semiclassical analysis of the average photon number as well as photon number variance (Fano factor F)F)F) for a Josephson junction (JJ) embedded microwave cavity system, where the JJ is subject to a fluctuating (i.e., noisy) bias voltage with finite dc average. Through the ac Josephson effect, the dc voltage bias drives the effectively nonlinear microwave cavity mode into an amplitude squeezed state (F<1)(F<1)(F<1), as has been established previously [Armour et al., Phys. Rev. Lett. 111, 247001 (2013)], but bias noise acts to degrade this squeezing. We find that the sensitivity of the Fano factor to bias voltage noise depends qualitatively on which stable fixed point regime the system is in for the corresponding classical nonlinear steady-state dynamics. Furthermore, we show that the impact of voltage bias noise is most significant when the cavity is excited to states with large average photon number.
A study of the Andreev level current through a weakly voltage-biased single-mode superconducting quantum point contact under microwave irradiation is presented. The applied microwave field induces resonant transitions between the current carrying Andreev states localized to the contact region, which results in an increase of the dc subgap current by several orders of magnitude. The applied voltage-bias couples to the superconductor phase difference across the junction, which will evolve in time. In turn the Andreev levels will oscillate adiabatically within the superconductor energy gap. Depending on the frequency of the applied field there can be either one or two resonances per oscillation period. When considering the case of two resonances the calculated dc-current exhibits an interference pattern as a function of inverse voltage. A measurement of the oscillation period would make it possible to reconstruct the Andreev level spectrum. Further, a detailed study is conducted concerning the microwave-induced current as a function of voltage bias, and the amplitude and frequency of the applied field. In realistic experimental situations there are equilibrium fluctuations of the applied voltage bias and sometimes impurity induced noise in the contact transparency. The amount of dephasing induced on the interference pattern by these fluctuations is estimated. In most cases the interference pattern will be subject to some amount of decay. However, there are parameter values for which this decay will be small. The decay originating from equilibrium fluctuations is predicted to have a non-monotonic dependence on the position of the resonances, while the decay induced by impurities should increase linearly when the separation between the resonances is increased. This difference could be used to distinguish between the two sources. The results also indicate that it should be possible to experimentally investigate the coupling between Andreev states and their environment, explicitly the impedance which the contact "sees" and the coupling strength between impurities and Andreev states.