Left-handed superlattice metamaterials for circuit QED

Abstract

Quantum simulations is a promising field where a controllable system is used to mimic another system of interest, whose properties one wants to investigate. One of the key issues for such simulations is the ability to control the environment the system couples to, be it to isolate the system or to engineer a tailored environment of interest. One strategy recently put forward for environment engineering is the use of metamaterials with negative index of refraction. Here we build on this concept and propose a circuit-QED simulation of many-body Hamiltonians using superlattice metamaterials. We give a detailed description of a superlattice transmission line coupled to an embedded qubit, and show how this system can be used to simulate the spin-boson model in regimes where analytical and numerical methods usually fail, e.g. the strong coupling regime.

Coupling a Superconducting Qubit to a Left-Handed Metamaterial Resonator

“…In addition to increasing the coupling capacitance and resonator impedance, the length of the RHTL portion also impacts the coupling strength through the variation of the standing-wave amplitude at the location of the qubit. Besides increasing g i , we can also decrease ∆ω i by adding more unit cells to the LHTL or by using a superlattice arrangement for the LHTL [8], both of which increase the mode density since the number of modes between the IR and UV cutoff frequencies corresponds to the number of unit cells. Table III summarizes the various parameters for our hypothetical qubit-metamaterial device capable of achieving g i /∆ω i > 1.…”

“…For systems with multiple modes coupled to a qubit, there is the possibility of analog quantum simulation with photons in the different modes, allowing for the realization of a quantum model in a controlled platform [5]. As one example, the light-matter interaction Hamiltonian at large coupling strengths lends itself to the realization of the spin-boson model [6][7][8], a paradigmatic model of quantum dissipation and quantum phase transitions. Multi-mode cQED can also be used for studying qubit dynamics in the vicinity of photonic bandgaps [9,10], analogous to experiments using real atoms and photonic crystals [11].…”

Mode Structure in Superconducting Metamaterial Transmission-Line Resonators

“…An alternative approach, which we explore in a cQED architecture here, utilizes a periodic array of superconducting lumped-element reactances to engineer a onedimensional metamaterial in the microwave range [17,18]. This metamaterial is characterized by a photonic bandgap at low frequencies, with a band characterized by a lefthanded dispersion relation [19][20][21][22] and a dense set of modes at frequencies just above the bandgap, commensurate with superconducting qubit transition energies.…”

QSystem: bitwise representation for quantum circuit simulations

“…In this scenario, the simulation of quantum dynamics and small quantum circuits in a classical computer is of central importance. These may be used to validate computing models [11,12], simulate physical theories [13][14][15][16][17] and even to define the break-even point, when quantum computers match what is classically achievable [18]. To this end, several quantum circuit simulators have been developed in the past years, both from academic and industrial players [19][20][21][22][23][24][25][26].…”

“…(a) Benchmark for the preparation of entangled registers, Equation(15). (b) Benchmark for measurement of all qubits for an initial state given by Equation(14).…”