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arXiv:2202.05824 · Physical Review A

Bell-inequality violation by dynamical Casimir photons in a superconducting microwave circuit

Riddhi Chatterjee, A. S. Majumdar

Published Oct 31, 2022• 7 citations
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Abstract

We study the Bell's inequality violation by dynamical Casimir radiation with pseudospin measurement. We consider a circuit quantum electrodynamical setup where a relativistically moving mirror is simulated by variable external magnetic flux in a superconducting quantum interference device terminating a superconducting-microwave waveguide. We analytically obtain expectation values of the Bell operator optimized with respect to channel orientations in terms of the system parameters. We consider the effects of local noise in the microwave field modes, asymmetry between the field modes resulting from nonzero detuning, and signal loss. Our analysis provides ranges of the above experimental parameters for which the Bell violation can be observed. We show that the Bell violation can be observed in this setup up to $40\phantom{\rule{0.16em}{0ex}}\text{mK}$ temperature as well as up to 65% signal loss.

DOI
10.1103/physreva.106.042224

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We study the Bell's inequality violation by dynamical Casimir radiation with pseudospin measurement. We consider a circuit quantum electrodynamical setup where a relativistically moving mirror is simulated by variable external magnetic flux in a superconducting quantum interference device terminating a superconducting-microwave waveguide. We analytically obtain expectation values of the Bell operator optimized with respect to channel orientations in terms of the system parameters. We consider the effects of local noise in the microwave field modes, asymmetry between the field modes resulting from nonzero detuning, and signal loss. Our analysis provides ranges of the above experimental parameters for which the Bell violation can be observed. We show that the Bell violation can be observed in this setup up to 40mK40\phantom{\rule{0.16em}{0ex}}\text{mK}40mK temperature as well as up to 65% signal loss.
We theoretically investigate the dynamical Casimir effect (DCE) in electrical circuits based on superconducting microfabricated waveguides with tunable boundary conditions. We propose implementing a rapid modulation of the boundary conditions by tuning the applied magnetic flux through superconducting quantum-interference devices that are embedded in the waveguide circuits. We consider two circuits: (i) An open waveguide circuit that corresponds to a single mirror in free space, and (ii) a resonator coupled to a microfabricated waveguide, which corresponds to a single-sided cavity in free space. We analyze the properties of the DCE in these two setups by calculating the generated photon-flux densities, output-field correlation functions, and the quadrature squeezing spectra. We show that these properties of the output field exhibit signatures unique to the radiation due to the DCE, and could, therefore, be used for distinguishing the DCE from other types of radiation in these circuits. We also discuss the similarities and differences between the DCE, in the resonator setup, and the down-conversion of pump photons in parametric oscillators.
We investigate quantum correlations in microwave radiation produced by the dynamical Casimir effect in a superconducting waveguide terminated and modulated by a superconducting quantum interference device. We apply nonclassicality tests and evaluate the entanglement for the predicted field states. For realistic circuit parameters, including thermal background noise, the results indicate that the produced radiation can be strictly nonclassical and can have a measurable amount of intermode entanglement. If measured experimentally, these nonclassicality indicators could give further evidence of the quantum nature of the dynamical Casimir radiation in these circuits.
We investigate the dynamical Casimir effect in a coplanar waveguide (CPW) terminated by a superconducting quantum interference device (SQUID). Changing the magnetic flux through the SQUID parametrically modulates the boundary condition of the CPW, and thereby, its effective length. Effective boundary velocities comparable to the speed of light in the CPW result in broadband photon generation which is identical to the one calculated in the dynamical Casimir effect for a single oscillating mirror. We estimate the power of the radiation for realistic parameters and show that it is experimentally feasible to directly detect this nonclassical broadband radiation.
A fundamental property of the quantum vacuum is that a time-varying boundary condition for the electro-magnetic field can generate photons from the vacuum, the so-called the dynamical Casimir effect (DCE). The photons are created pairwise and should possess the particular quantum correlations referred to as entanglement. In particular, broadband entanglement sources are useful for two reasons: i) they can be very bright, generating a large number of entangled photons, and ii) the wide frequency content allows shaping the emitted radiation in time. Here we present the observation of entanglement generated in a broadband system using the DCE. The measured sample consists of a superconducting quantum interference device (SQUID) terminating a microwave transmission line. A magnetic flux modulates the SQUID's Josephson inductance at approximately 9~GHz, resulting in a time-varying boundary condition for the quantum vacuum in the transmission line. We detect both quadratures of the microwave radiation emitted at two different frequencies separated by 0.7~GHz. Analysing the measured data and using a careful calibration of the power level emitted from the sample, we determine the purity and type of entanglement using two different methods. We estimate an entanglement rate of 5~Mebit/s (mega entangled bits per second).
Superconducting microwave circuits provide a versatile platform for studying quantum optics with artificial atoms, mainly motivated by applications in quantum information. In addition, the circuits are promising for simulation of relativistic phenomena. This thesis is based on theoretical work along both these lines.Firstly, we consider a transmon coupled to an open transmission line. Using circuit quantization techniques and the master equation formalism, we theoretically describe scattering of coherent microwaves states on the transmon. The results agree with various recent experiments. As an example, we see a photon number redistribution leading to antibunching in the reflected field and superbunching in the transmitted field. Inspired by these results, we further investigate the possibility of generating single-photon states on demand in the system. We find that a single two-level system in an open transmission line is not a suitable single-photon source. With an asymmetric setup using two transmission lines, however, single-photon probabilities close to unity can be achieved.Secondly, we investigate simulation of a relativistically moving cavity containing a quantum field.Previously, in order to demonstrate the dynamical Casimir effect, a SQUID was used to tune a boundary condition in a way that mimics a moving mirror. Building on this idea, we extend the setup and use two SQUIDs to simulate the moving cavity. An experiment is proposed where the cavity is used as a clock and we show that time dilation should be observable for realistic circuit parameters. We also show how the size and the acceleration of the clock leads to a deviation from the ideal clock formula. Moreover, the effect of acceleration on the precision of the clock is analyzed.
When one of the parameters in the Euler-Lagrange equations of motion of a system is modulated, particles can be generated out of the quantum vacuum. This phenomenon is known as the dynamical Casimir effect, and it was recently realized experimentally in systems of superconducting circuits, for example by using modulated resonators made of coplanar waveguides, or arrays of superconducting quantum intereference devices (SQUIDs) forming a Josephson metamaterial. In this paper, we consider a simple electrical circuit model for dynamical Casimir effects, consisting of an LC resonator, with the inductor modulated externally at 10.8 GHz and with the resonant frequency tunable over a range of ±\pm± 400 MHz around 5.4 GHz. The circuit is analyzed classically using a circuit simulator (APLAC). We demonstrate that if an additional source of classical noise couples to the resonator (on top of the quantum vacuum), for example via dissipative "internal modes", then the resulting spectrum of the photons in the cavity will present two strongly asymmetric branches. However, according to the theory of the dynamical Casimir effect, these branches should be symmetric, a prediction which is confirmed by our experimental data. The simulation presented here therefore shows that the origin of the photons generated in our experiment with Josephson metamaterials is the quantum vacuum, and not a spurious classical noise source.