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arXiv:1401.7875

Photon Generation from Quantum Vacuum using a Josephson Metamaterial

Pasi Lähteenmäki, Gheorghe Sorin Paraoanu, Juha Hassel, Pertti Juhani Hakonen

Published Jan 30, 2014• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.1401.7875

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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.
When one of the parameters in the Euler-Lagrange equations of motion of a sys- tem is modulated, particles can be generated out of the quantum vacuum. This phenomenon is known as the dynamical Casimir efiect, and it was recently realized experimentally in systems of superconducting circuits, for example by using modulated resonators made of coplanar waveg- uides, 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 efiects, consisting of an LC resonator, with the inductor modulated externally at 10.8GHz and with the resonant frequency tunable over a range of §400MHz around 5.4GHz. 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 efiect, these branches should be symmetric, a prediction which is conflrmed by our ex- perimental 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. The picture about vacuum that emerges from modern quantum fleld theory is very difierent from that ofiered by classical physics. In classical fleld theory, the vacuum is the zero-energy state of the fleld, deflned by the absence of any excitation. In quantum fleld theory, the vacuum state has a flnite zero-point energy associated with it, and the uncertainty principle indicates that ∞uctuations exist even in this state. Due to the existence of ∞uctuations, the quantum vacuum can become unstable under certain perturbations, and the energy of the perturbation is converted into creation of real particles (1). In the Schwinger efiect for example, a static intense electric fleld can create pairs of electrons and positrons. In very strong gravitational flelds, at the event horizon of black holes, the vacuum becomes unstable and energy is radiated away (Hawking efiect). By the equivalence principle, an accelerated observer in the Minkowski vacuum will detect a flnite-temperature fleld (Unruh efiect). In a previous paper, we reported the observation of the dynamical Casimir efiect using a ∞ux- biased Josephson metamaterial embedded in a microwave cavity at 5.4GHz (2). A non-adiabatic change in the index of refraction of the cavity (or in the electrical length) was realized by modulat- ing the ∞ux at values close to double the resonant frequency of the cavity. We measured also the frequency-correlated photons emitted from the cavity (which is kept at a temperature T = 50mK), and we obtained a power spectrum displaying a bimodal, \sparrow-tail distribution, with two sym- metric branches. Furthermore, we demonstrated that the generated photons are squeezed below the vacuum level and that the state of the two-photon fleld is nonseparable. The experimental results are in excellent agreement with the theoretical predictions. An alternative realization of the dynam- ical Casimir efiect consists in modulating an efiective boundary condition, realized experimentally as a SQUID structure placed at the end of a coplanar waveguide resonator (3). Remarkably, the experiments presented in Refs. (2,3) are the only existing measurements of the dynamical Casimir efiect, which was predicted theoretically in 1970 (4).
In November 2011 the first experimental observation of the dynamical Casimir effect was published [1]. Superconducting circuits were used to show that a single mirror moving in vacuum could generate photons, by parametric amplification of vacuum uctuations. This project is a side track of this research where a second mirror is introduced to investigate photon generation in-between the mirrors. The work includes both theory studies and experimental practice. Resonators have been fabricated on chip in a cleanroom and measured in a dilution refrigerator. The focus has been on how the different boundary conditions of the resonator field affect the photon generation. A superconducting circuit has been used including a = 2/2 resonator with two SQUIDs inducing tunability of the resonance frequency via on-chip ux tuning lines. The two SQUIDs are placed in each end of the cavity in order to simulate moving mirrors. The mirrors are used to modulate the boundary conditions of the cavity. This is done by changing the SQUID inductance which is achieved by applying a magnetic ux to the SQUID loop. Depending on if the mirrors move in or out of phase, a breathing or translational mode can be created in the cavity. Theory predicts photon generation in different modes depending on if the pump frequency is two or three times the resonance frequency [2]. Measurements have been done at a temperature of around 50mK, which is low enough to have a negligible amount of thermal photons and quasi-particles in the cavity. The static tuning of the resonator have been probed by sweeping the uxes applied to the two SQUIDs and at each point the resonance frequency has been extracted. Good results have been achieved and two dimensional tuning is shown. A high frequency, ux modulation have been applied to the SQUIDs both one at a time and simultaneously to generate photons. In the two mirror modulation case qualitative agreement with theory has been observed for driving in the breathing and translational mode respectively. Generation occurs first for the breathing mode at 2*omega (twice the resonance frequency) and for the translational mode at 3*omega.
Abstract Real photon pairs can be created in a dynamic cavity with an oscillating boundary or temporally modulated refractive index of the constituent medium. This effect is called dynamic Casimir effect (DCE), which represents one of the most amazing predictions of quantum field theory. The DCE has been experimentally observed in Josephson metamaterials embedded in a microwave cavity. However, the efficiency of the observed DCE is extremely weak, entailing a complex external signal enhancement process to detect the signal. Here, it is shown that the DCE can be drastically enhanced in a dynamic 1D cavity consisting of a superconducting quantum interference device (SQUID)‐based Josephson transmission line with both temporal and spatial modulation on the effective inductance profile through flux‐biasing. Such a system can resonantly generate photons at driving frequencies equal to even or odd integer times of that of the fundamental cavity mode governed by the symmetry of the spatial modulation. Interesting spectral and scaling behaviors for photons excited at the band edge are further observed. The discovery introduces a new degree of freedom—spatial modulation—to enhance the efficiency of DCE.
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).
In this work we study simulations of photon generation due to the dynamical Casimir effect (DCE) in a one-dimensional ( 1 + 1 ) double superconducting cavity. To achieve this, we propose the use of a superconducting quantum circuit so as to be able to experimentally perform quantum simulations of the DCE. The simulated cavity consists of two perfectly conducting mirrors and a dielectric membrane of infinitesimal depth that effectively couples two cavities. The total length of the double cavity L , the difference in length between the two cavities Δ L , and the electric susceptibility χ and conductivity v of the dielectric membrane are tunable parameters. All four parameters are treated as independent and are allowed to be tuned at the same time, even with different frequencies. We analyze the cavity's energy spectra under different conditions, finding a transition between two distinct regimes that is accurately described by k c = v / χ . In particular, a lowest-energy mode is forbidden in one of the regimes while it is allowed in the other. We compare analytical approximations obtained through the multiple-scale analysis method with exact numerical solutions, obtaining the typical results when χ is not being tuned. However, when the susceptibility χ is tuned, different behaviors (such as oscillations in the number of photons of a cavity prepared in a vacuum state) can arise if the frequencies and amplitudes of all parameters are adequate. These oscillations might be considered as adiabatic shortcuts where all generated photons are eventually destroyed.
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.