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arXiv:1612.06774 · Physical Review A

Simulating superluminal physics with superconducting circuit technology

Carlos Sabín, Borja Peropadre, Lucas Lamata, E. Solano

Published Sep 27, 2017• 12 citations
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Abstract

We provide tools for the quantum simulation of superluminal motion with superconducting circuits. We show that it is possible to simulate the motion of a superconducting qubit at constant velocities that exceed the speed of light in the electromagnetic medium and the subsequent emission of Ginzburg radiation. We also consider possible setups for simulating the superluminal motion of a mirror, finding a link with the super-radiant phase transition of the Dicke model.

DOI
10.1103/physreva.96.032121

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•Jan 1, 2015•0 citations
We provide tools for the quantum simulation of superluminal motion with superconducting circuits. We show that it is possible to simulate the motion of a superconducting qubit at constant velocities that exceed the speed of light in the electromagnetic medium and the subsequent emission of Ginzburg radiation. We also consider possible setups for simulating the superluminal motion of a mirror, finding a link with the super-radiant phase transition of the Dicke model.
We present a scheme for simulating relativistic quantum physics in circuit quantum electrodynamics. By using three classical microwave drives, we show that a superconducting qubit strongly coupled to a resonator field mode can be used to simulate the dynamics of the Dirac equation and Klein paradox in all regimes. Using the same setup we also propose the implementation of the Foldy–Wouthuysen canonical transformation, after which the time derivative of the position operator becomes a constant of the motion.
We propose the analog-digital quantum simulation of the quantum Rabi and Dicke models using circuit quantum electrodynamics (QED). We find that all physical regimes, in particular those which are impossible to realize in typical cavity QED setups, can be simulated via unitary decomposition into digital steps. Furthermore, we show the emergence of the Dirac equation dynamics from the quantum Rabi model when the mode frequency vanishes. Finally, we analyze the feasibility of this proposal under realistic superconducting circuit scenarios.
We propose an implementation of a twin-paradox scenario in superconducting circuits, with velocities as large as a few percent of the speed of light. Ultrafast modulation of the boundary conditions for the electromagnetic field in a microwave cavity simulates a clock moving at relativistic speeds. Since our cavity has a finite length, the setup allows us to investigate the role of clock size as well as interesting quantum effects on time dilation. In particular, our theoretical results show that the time dilation increases for larger cavity lengths and is shifted due to quantum particle creation.
We propose a digital-analog quantum simulation of generalized Dicke models with superconducting circuits, including Fermi- Bose condensates, biased and pulsed Dicke models, for all regimes of light-matter coupling. We encode these classes of problems in a set of superconducting qubits coupled with a bosonic mode implemented by a transmission line resonator. Via digital-analog techniques, an efficient quantum simulation can be performed in state-of-the-art circuit quantum electrodynamics platforms, by suitable decomposition into analog qubit-bosonic blocks and collective single-qubit pulses through digital steps. Moreover, just a single global analog block would be needed during the whole protocol in most of the cases, superimposed with fast periodic pulses to rotate and detune the qubits. Therefore, a large number of digital steps may be attained with this approach, providing a reduced digital error. Additionally, the number of gates per digital step does not grow with the number of qubits, rendering the simulation efficient. This strategy paves the way for the scalable digital-analog quantum simulation of many-body dynamics involving bosonic modes and spin degrees of freedom with superconducting circuits.
Superconducting quantum circuit models are widely used to understand superconducting devices. This thesis consists of four studies wherein the superconducting quantum circuit is used to illustrate challenges related to quantum information encoding and processing, quantum simulation, quantum signal detection and amplification.The existence of scalar Aharanov-Bohm phase has been a controversial topic for decades. Scalar AB phase, defined as time integral of electric potential, gives rises to an extra phase factor in wavefunction. We proposed a superconducting quantum Faraday cage to detect temporal interference effect as a consequence of scalar AB phase. Using the superconducting quantum circuit model, the physical system is solved and resulting AB effect is predicted. Further discussion in this chapter shows that treating the experimental apparatus quantum mechanically, spatial scalar AB effect, proposed by Aharanov-Bohm, can't be observed. Either a decoherent interference apparatus is used to observe spatial scalar AB effect, or a quantum Faraday cage is used to observe temporal scalar AB effect.The second study involves protecting a quantum system from losing coherence, which is crucial to any practical quantum computation scheme. We present a theory to encode any qubit, especially superconducting qubits, into a universal quantum degeneracy point (UQDP) where low frequency noise is suppressed significantly. Numerical simulations for superconducting charge qubit using experimental parameters show that its coherence time is prolong by two orders of magnitude using our universal degeneracy point approach. With this improvement, a set of universal quantum gates can be performed at high fidelity without losing too much quantum coherence.Starting in 2004, the use of circuit QED has enabled the manipulation of superconducting qubits with photons. We applied quantum optical approach to model coupled resonators and obtained a four-wave mixing toolbox to operate photons states. The model and toolbox are engineered with a superconducting quantum circuit where two superconducting resonators are coupled via the UQDP circuit. Using fourth order perturbation theory one can realize a complete set of quantum operations between these two photon modes. This helps open a new field to treat photon modes as qubits. Additional, a three-wave mixing scheme using phase qubits permits one to engineer the coupling Hamiltonian using a phase qubit as a tunable coupler.Along with Feynman's idea using quantum to simulate quantum, superconducting quantum simulators have been studied intensively recently. Taking the advantage of mesoscopic size of superconducting circuit and local tunability, we came out the idea to simulate quantum phase transition due to disorder. Our first paper was to propose a superconducting quantum simulator of Bose-Hubbard model to do site-wise manipulation and observe Mott-insulator to superfluid phase transition. The side-band cooling of an array of superconducting resonators is solved after the paper was published. In light of the developed technology in manipulating quantum information with superconducting circuit, one can couple other quantum oscillator system to superconducting resonators in order manipulation of its quantum states or parametric amplification of weak quantum signal. A theory that works for different coupling schemes has been studied in chapter 5. This will be a platform for further research.