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.
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).
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 ± 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.
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.
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.
In this thesis I present different experiments on superconducting circuits exploring parametric interactions with external signals and the vacuum in the microwave regime. These parametric processes are the result of the periodic modulation of a property of a system which results in different interactions. The systems used in this thesis are circuits where the nonlinear inductance of a superconducting quantum interference device (SQUID) is parametrically driven.I present the first experimental observation of the dynamical Casimir effect (DCE), since it was predicted in 1970. The DCE is an interaction between the vacuum and a periodically modulated boundary condition of the electromagnetic field, here implemented by a flux-tuned SQUID. In essence the modulated boundary will parametrically amplify the vacuum fluctuations which results in the pairwise generation of photons over a broad frequency range. I have characterized the system and measured the statistical properties of the emitted radiation to show that the radiation exhibits two-mode squeezing.Next, I present measurements on a superconducting multimode resonator containing a SQUID. I show that it is possible to get parametric amplification by driving the SQUID at either twice the frequency of one of the modes or by driving it at the sum of two mode frequencies. In both cases I show that it is possible to reach quantum-limited noise performance.In the same system I also demonstrate frequency conversion which occurs when the system is pumped at the difference frequency between two modes. Microwave photons are coherently transferred from one mode to the other. I show that the coupling strength depends linearly on the applied pump amplitude.The thesis also contains a linearized theoretical model to describe and analyze the flux-pumped SQUID. The model describes an equivalent circuit element called the pumpistor, with an impedance which depends on the pump phase. I show that under specific conditions the impedance becomes real and negative allowing pump power to be injected into the circuit, providing gain.Finally I also present a demonstration of an on-chip Mach-Zehnder interferometer. This experiment uses the tunability of the SQUID to provide a controllable phase shift in one of the interferometer arms. The transmission through the device can be modulated with a maximum change of 45 dB.