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arXiv:1402.7185 · New Journal of Physics

Simulating systems of itinerant spin-carrying particles using arrays of superconducting qubits and resonators

Sahel Ashhab

Published Oct 30, 2014• 9 citations
arXivHTMLPDF

Abstract

We propose possible approaches for the quantum simulation of itinerant spin-carrying particles in a superconducting qubit-resonator array. The standard Jaynes–Cummings–Hubbard setup considered in several recent studies can readily be used as a quantum simulator for a number of relevant phenomena, including the interaction with external magnetic fields and spin-orbit coupling. A more complex setup where multiple qubits and multiple resonator modes are utilized in the simulation gives a higher level of complexity, including the simulation of particles with high spin values, and it allows more direct control on processes related to spin-orbit coupling. This proposal could be implemented in state-of-the-art superconducting circuits in the near future.

DOI
10.1088/1367-2630/16/11/113006

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We propose possible approaches for the quantum simulation of itinerant spin-carrying particles in a superconducting qubit-resonator array. The standard Jaynes–Cummings–Hubbard setup considered in several recent studies can readily be used as a quantum simulator for a number of relevant phenomena, including the interaction with external magnetic fields and spin-orbit coupling. A more complex setup where multiple qubits and multiple resonator modes are utilized in the simulation gives a higher level of complexity, including the simulation of particles with high spin values, and it allows more direct control on processes related to spin-orbit coupling. This proposal could be implemented in state-of-the-art superconducting circuits in the near future.
Abstract The Jaynes‐Cummings model describes the coupling between photons and a single two‐level atom in a simplified representation of light‐matter interactions. In circuit QED, this model is implemented by combining microwave resonators and superconducting qubits on a microchip with unprecedented experimental control. Arranging qubits and resonators in the form of a lattice realizes a new kind of Hubbard model, the Jaynes‐Cummings‐Hubbard model, in which the elementary excitations are polariton quasi‐particles. Due to the genuine openness of photonic systems, circuit QED lattices offer the possibility to study the intricate interplay of collective behavior, strong correlations and non‐equilibrium physics. Thus, turning circuit QED into an architecture for quantum simulation, i.e., using a well‐controlled system to mimic the intricate quantum behavior of another system too daunting for a theorist to tackle head‐on, is an exciting idea which has served as theorists’ playground for a while and is now also starting to catch on in experiments. This review gives a summary of the most recent theoretical proposals and experimental efforts.
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We propose a superconducting circuit platform for simulating spin-1 models. To this purpose we consider a chain of NNN ultrastrongly coupled qubit-resonator systems interacting through a grounded superconducting quantum interference device (SQUID). The anharmonic spectrum of the qubit-resonator system and the selection rules imposed by the global parity symmetry allow us to activate well controlled two-body quantum gates via ac pulses applied to the SQUID. We show that our proposal has the same simulation time for any number of spin-1 interacting particles. This scheme may be implemented within the state-of-the-art circuit QED in the ultrastrong coupling regime.
We describe a superconducting-circuit lattice design for the implementation and simulation of dynamical lattice gauge theories. We illustrate our proposal by analyzing a one-dimensional U(1) quantum-link model, where superconducting qubits play the role of matter fields on the lattice sites and the gauge fields are represented by two coupled microwave resonators on each link between neighboring sites. A detailed analysis of a minimal experimental protocol for probing the physics related to string breaking effects shows that, despite the presence of decoherence in these systems, distinctive phenomena from condensed-matter and high-energy physics can be visualized with state-of-the-art technology in small superconducting-circuit arrays.
We consider superconducting circuits for the purpose of simulating the spin-boson model. The spin-boson model consists of a single two-level system coupled to bosonic modes. In most cases, the model is considered in a limit where the bosonic modes are sufficiently dense to form a continuous spectral bath. A very well known case is the Ohmic bath, where the density of states grows linearly with the frequency. In the limit of weak coupling or large temperature, this problem can be solved numerically. If the coupling is strong, the bosonic modes can become sufficiently excited to make a classical simulation impossible. Here we discuss how a quantum simulation of this problem can be performed by coupling a superconducting qubit to a set of microwave resonators. We demonstrate a possible implementation of a continuous spectral bath with individual bath resonators coupling strongly to the qubit. Applying a microwave drive scheme potentially allows us to access the strong-coupling regime of the spin-boson model. We discuss how the resulting spin relaxation dynamics with different initialization conditions can be probed by standard qubit-readout techniques from circuit quantum electrodynamics.
We consider a superconducting charge qubit coupled to distinct orthogonal electromagnetic field modes belonging to a coplanar wave guide and a microstrip transmission line resonators. This architecture allows the simultaneous implementation of a Jaynes-Cummings and anti-Jaynes-Cummings dynamics, a resonant method for generating mesoscopic qubit-field superpositions and for field-state reconstruction. Furthermore, we utilize this setup to propose a field measurement technique that is, in principle, robust to qubit dephasing and field relaxation due to a fast pre-measurement.