Circuit Quantum Electrodynamics Mark David Jenkins Martes cúantico, February 25th, 2014
Introduction Theory details Strong coupling experiment Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation, A. Blais, R.-S. Huang, A. Wallraff, S.M. Girvin and R.J. Shoelkopf, Physical Review A 69, 062320 (2004) Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics, A. Wallraff, D.I. Schuster, A. Blais, L. Frunzio, R.-S Huang, J. Majer, S. Kumar, S.M. Girvin and R.J. Schoelkopf, Nature 431, p162 (2004) General review: Wiring up quantum systems, R.J. Schoelkopf and S.M. Girvin, Nature 451, p644 (2008) 2/35
Introduction Objective: Quantum Information processing Combine quantum mechanics and computers Superposition and entanglement lead to a kind of parallel processing Allows for increased computational power 3/35
Introduction Challenges: Bits must be replaced with qubits Mechanism to manipulate qubits One-qubit operations Quantum logic gates Quantum bus Reduce decoherence Quantum 2 level systems Quantum states are extremely fragile Competes with ease of manipulation 4/35
Introduction Physical implementations for Qubits Natural candidates Atoms, ions, nuclei, spins Synthetic candidates Quantum dots Superconducting circuits Voltages and currents exhibit quantum behaviour Fabricated using techniques from conventional electronics 5/35
Introduction The main means to interact with any of these systems is through electromagnetic radiation Photons are naturally quantum objects Can be transmitted over large distances without being lost Cavity QED Prototype of quantum lightmatter interaction 6/35
Cavity QED Simple case: Single atom with two energy levels coupled to a single mode of the EM field Can be coupled to the electric or magnetic field 7/35
Cavity QED Resonator / Cavity = Harmonic Osillator Quantum equivalent Two level system 8/35
Cavity QED Jaynes-Cummings Hamiltonian Cavity Atom Interaction Losses 9/35
Cavity QED Vacuum Rabi frequency ( ) Strength of the interaction System oscillates between Given by ) Resonance frequencies (or and Detuning Damping Loss of photons from the cavity ( ) Decay into undesired modes ( ) Strong coupling regime Quantum information can be exchanged from atom to photon 10/35
Cavity QED Solving in absence of damping: 11/35
Cavity QED Solving in absence of damping: 12/35
Cavity QED Challenge: Maximize g while minimizing Theoretical limit (electric coupling) 13/35
Circuit QED Circuit QED = Cavity QED on a chip Cavity is replaced with superconducting coplanar waveguide resonator (1D cavity) Atom is replaced with superconducting qubit 14/35
CPWG resonator Relevant parameters: Length ( ) Dielectric constants Easy to fabricate In a single plane Standard lithographic techniques Q factors of up to 106 Microwave frequencies (GHz) 15/35
CPWG resonator 16/35
Superconducting qubits Based on Josephson Junctions Nonlinear inductor Harmonic oscillator Types: Cooper pair box (d) Flux qubit (e) Couples to E field Couples to B field Phase qubit (f) 17/35
Superconducting qubits Cooper pair box Basic hamiltonian: Electric energy Josephson energy 18/35
Circuit QED Combined system reduces (under good approximations) to the Jaynes-Cummings hamiltonian. At the charge degeneracy point ( At other biases these values are modulated Typical losses are Number of operations ): 19/35
Circuit QED 20/35
Circuit QED Zero detuning Transmission at single photon level Large detuning Lifetime enhancement From 1 μs to 64 μs QND readout Coherent control Non-linear effects 21/35
Dispersive QND readout Large detuning Cavity frequency is pulled by In theses cases, the probability of real transitions is small 22/35
Dispersive QND readout 23/35
Dispersive QND readout Driving the cavity induces some dephasing and coherent mixing Calculations for dephasing yield Quantum limit is not reached ( ) Non adiabatic coupling Reflected wave contains missing information Coherent mixing for given parameters Reversible 24/35
Coherent control Irradiation at: Resonator frequency is a measurement Qubit frequency is a rotation 25/35
Coherent control With given parameters: Low photon population Virtually populated Fast response 1 qubit gate 26/35
Quantum bus It is possible to place several qubits along the resonator at the nodes of the electric field The resonator acts as a quantum bus Hamiltonian has terms Allows entanglement of the different qubits operation Possible 2 qubit readout 1200 operations with given parameters Different detunings on each allows 4 different cavity pulls 27/35
Strong coupling experiment Device: 28/35
Strong coupling experiment Measurement scheme 29/35
Strong coupling experiment Qubit parameter determination 30/35
Strong coupling experiment Vacuum rabi splitting 31/35
Further experiments 32/35
Other quantum bits? 33/35
Stronger couplings? Magnetic systems have generally weaker couplings but better coherence Ensambles can be used to achieve strong coupling Coupling can be enhanced by moving closer to the currents Done with NV centers Superconductors have superficial currents and can allow thinner wires 34/35
Stronger couplings? 35/35