We propose the use of a waveguidelike transmission line based on direct-current superconducting quantum interference devices (dc-SQUID) and demonstrate that the node flux in this transmission line behaves in the same way as quantum fields in an expanding (or contracting) universe. We show how to detect the analog cosmological particle generation and analyze its feasibility with current circuit quantum electrodynamics (cQED) technology. Our setup in principle paves a new way for the exploration of analog quantum gravitational effects.
We propose the use of a waveguidelike transmission line based on direct-current superconducting quantum interference devices (dc-SQUID) and demonstrate that the node flux in this transmission line behaves in the same way as quantum fields in an expanding (or contracting) universe. We show how to detect the analog cosmological particle generation and analyze its feasibility with current circuit quantum electrodynamics (cQED) technology. Our setup in principle paves a new way for the exploration of analog quantum gravitational effects.
Quantum optics in superconducting circuits, known as circuit QED, studies the interaction of photons at microwave frequencies with artificial atoms made of Josephson junctions. Although quite young, remarkable progress has been made in this field over the past decade, especially given the interest in building a quantum computer using superconducting circuits. In this thesis based on the appended papers, we look at generation, engineering and detection of microwave photons using superconducting circuits. We do this by taking advantage of the strong coupling, on-chip tunability and huge nonlinearity available in superconducting circuits. First, we present the strong photon-photon interaction measured experimentally, as shown in the giant cross-Kerr effect. In this work, conditional phase shift of about 20 degrees per photon was measured between two coherent fields at single photon level. Given this strong interaction, we propose and analyze a cascaded setup based on the cross-Kerr effect to detect itinerant microwave photons, a long outstanding problem with only recent experimental realizations. We show that a nondestructive detection of microwave photons is possible with few cascaded transmons. The on-chip tunability of Superconducting Quantum Interference Device (SQUID) is exploited to create a tunable superconducting resonator in the next presented experimental work. Finally, we show that by placing the atom at the end of a transmission line, microwave photons can be generated efficiently and on-demand. We also present a setup that can generate the photons in arbitrary wave packets.
We describe a new dc-superconducting quantum interference device (SQUID) circuit of the FM type, which has a large coefficient for converting an applied magnetic flux into a frequency of MHz band or a lower band. The circuit consists of a SQUID amplifier composed of two stages, formed by a superconducting weak link and two dc-SQUID elements with nonhysteretic characteristics. In the first stage, the weak link and dc-SQUID elements are connected in parallel and operated by a common bias voltage. Since the respective elements oscillate with high frequencies by the ac Josephson effect, the two frequencies interact with each other, so that, the first stage generates a beat signal of a lower frequency. In the second stage, the other dc-SQUID element with a intrinsic flux gain enhances the beat signal generated during the first stage. A theoretical analysis of the circuit with computer simulation shows that the beat frequency is a periodical function of the magnetic flux, and the SQUID amplifier with two stages can improve the flux sensitivity.
We investigate a quantum-circuit analog of the dynamical Casimir effect discussed in cavity quantum electrodynamics (QED). A double superconducting quantum interference device (SQUID), consisting of a superconducting loop interrupted by a dc-SQUID, is regarded as a harmonic oscillator with a time-dependent frequency imitating the nonadiabatic boundaries in a cavity QED. Squeezing occurs due to parametric processes inherent in the system. We reformulate squeezing based on the Bogoliubov transformation between eigenstates at different times and derive the analytic formula for quantum-state evolutions of the system. The squeezing parameter clearly reveals the relationship between squeezing and nonadiabatic nature of the system. Thus, the squeezing parameter serves as a measure for the dynamical Casimir effect. We demonstrate squeezing for two types of frequency modulation and propose a method for measuring squeezing by using a circuit QED technique under coherent oscillations between an artificial atom and an LC circuit in the presence of dissipation. These observations suggest that a quantum circuit with a Josephson junction is a promising candidate for detecting the dynamical Casimir effect.
Circuit Quantum Electrodynamics (cQED), the study of the interaction between superconducting circuits behaving as artificial atoms and 1-dimensional transmission-line resonators, has shown much promise for quantum information processing tasks. For the purposes of quantum computing it is usual to approximate the artificial atoms as 2-level qubits, and much effort has been expended on attempts to isolate these qubits from the environment and to invent ever more sophisticated control and measurement schemes. Rather than focussing on these technological aspects of the field, this thesis investigates the opportunities for using these carefully engineered systems for answering questions of fundamental physics.
Integrating two-dimensional (2D) materials into circuit quantum electrodynamics (cQED) devices is an emerging field in recent years. This integration not only facilitates the exploration of potential applications in quantum information processing but also enables the study of material's fundamental properties using microwave techniques. While most studies employ 2D coplanar architectures with scalability potential, three-dimensional (3D) cavity-based cQED devices, due to their simpler design, offer the advantage of a quicker turnaround to probe the composite Josephson junctions (JJs). Here, we construct the first flux-tunable, 3D cavity-compatible superconducting quantum circuit based on 2D materials, featuring a graphene superconducting quantum interference device (SQUID) shunted by a capacitor that is accessible by both dc and microwave probes. We have shown how flux-modulated cavity frequency can be linked to the SQUID critical current under the influence of Fraunhofer's pattern. In addition, we extracted the symmetry information of the SQUIDs based on dc analysis, and correlated this with the flux-modulated cavity frequency observed in microwave measurements. Our platform can extend to topological materials, holding the prospect of establishing valid topological JJs with a dc probe while allowing a fast microwave probe to avoid quasiparticle poisoning.
In recent years, superconducting circuits have come to the forefront of certain areas of physics. They have shown to be particularly useful in research related to quantum computing and information, as well as fundamental physics. This is largely because they provide a very flexible way to implement complicated quantum systems that can be relatively easily manipulated and measured. In this thesis we look at three different applications where superconducting circuits play a central role, and explore their classical and quantum dynamics and behavior. \n \nThe first part consists of studying the Casimir [Proc. K. Ned. Akad. Wet (1948)] and Casimir-Polder like [Physical Review 73, 4 (1948)]effects. These effects have been discovered in 1948 and show that under certain conditions, vacuum field fluctuations can mediate forces between neutral objects. In our work, we analyze analogous behavior in a superconducting system which consists of a stripline cavity with a DC-SQUID on one of its boundaries, as well as, in a Casimir-Polder case, a charge qubit coupled to the field of the cavity. Instead of a force, in the system considered here, we show that the Casimir and Casimir-Polder like effects are mediated through a circulating current around the loop of the boundary DC-SQUID. Using detailed analysis, we examine how the values of these currents change as we vary different physical circuit parameters. We show that for the set of physical parameters that can be easily obtained experimentally, the Casimir and Casimir-Polder currents can be of the order of 10^(-8) A and 10^(-13) A respectively. \n \nIn the second part, we theoretically model an experiment which was performed by Britton Plourde's group at Syracuse University, and which studied the transient dynamics of a nonlinear superconducting oscillator, based on a capacitively shunted DC-SQUID. Such DC-SQUID oscillators are used in many areas of physics and engineering, for example, as building blocks of amplifiers or qubits, qubit couplers, or as sensitive magnetic field detectors. In many of these situations, their steady state behavior is often considered, while in the experiment performed at Syracuse, of specific interest, was the response of a DC-SQUID oscillator to a short radiation that only briefly excited the system. In this thesis, we simulate this response at the experimental temperature, by numerically solving a set of classical stochastic differential equations that mimic the behavior of the circuit. This is done for different settings of the flux that is threaded through the DC-SQUID as well as different input pulse amplitudes. Furthermore, we briefly outline just how these kinds of brief excitations could be useful when applied in flux measurement protocols. We find that our simulations show good agreement with the experimentally obtained data. \n \nThe final part considered in this thesis, looks at the dynamics of a qubit coupled to a measuring probe, which is modeled as a harmonic oscillator. An example superconducting circuit, that could be used to implement such a setup, consists of a flux qubit inductively coupled to a DC-SQUID. This measurement scenario has already been explored in [Phys. Rev. B 78, 5 (2008)], but there, the authors only consider very short interaction times between the DC-SQUID and the qubit. Here, in contrast, we concentrate our efforts on studying the evolution of qubit as the measurement takes place, by solving the corresponding Lindblad master equation, but over longer measurement times. This is done by calculating the measurement induced dephasing rate of the qubit, as well as, discussing its sometimes present effective relaxation, in regimes where the measurement is considered to not be quantum non-demolition (QND). Finally, we briefly explore how well a potentially complicated evolution of the qubit can be approximated as a very simple Kraus map.