Circuit Quantum Circuit Quantum ElectrodynamicsElectrodynamics

Mark David JenkinsMark David Jenkins

““Martes cúantico”, February 25Martes cúantico”, February 25thth, 2014, 2014

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Introduction

● Theory details

– “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 experiment

– “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)

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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

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Introduction

● Challenges:– Bits must be replaced with qubits

● Quantum 2 level systems

– Mechanism to manipulate qubits● One-qubit operations● Quantum logic gates● Quantum bus

– Reduce decoherence● Quantum states are extremely fragile● Competes with ease of manipulation

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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

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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 light-matter interaction

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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

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Cavity QED● Resonator / Cavity = Harmonic Osillator

● Quantum equivalent

● Two level system

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Cavity QED

● Jaynes-Cummings Hamiltonian

Cavity Atom Interaction Losses

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Cavity QED

● Vacuum Rabi frequency ( )– Strength of the interaction

– System oscillates between and

– Given by (or )

● Resonance frequencies – Detuning

● Damping– Loss of photons from the cavity ( )

– Decay into undesired modes ( )

● Strong coupling regime -– Quantum information can be exchanged from atom to photon

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Cavity QED

● Solving in absence of damping:

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Cavity QED

● Solving in absence of damping:

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Cavity QED

● Challenge: Maximize g while minimizing ● Theoretical limit (electric coupling)

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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

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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)

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CPWG resonator

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Superconducting qubits

● Based on Josephson Junctions– Nonlinear inductor – Harmonic oscillator

● Types:– Cooper pair box (d)

● Couples to E field

– Flux qubit (e)● Couples to B field

– Phase qubit (f)

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Superconducting qubits

● Cooper pair box ● Basic hamiltonian:

– Electric energy– Josephson energy

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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

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Circuit QED

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Circuit QED

● Zero detuning– Transmission at

single photon level

–

–

–

–

– Non-linear effects

● Large detuning– Lifetime enhancement

● From 1 μs to 64 μs

– QND readout

– Coherent control

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Dispersive QND readout

● Large detuning● Cavity frequency is pulled by

● In theses cases, the probability of real transitions is small

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Dispersive QND readout

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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

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Coherent control

● Irradiation at:– Resonator frequency is a measurement

– Qubit frequency is a rotation

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Coherent control

● With given parameters:

● Low photon population– “Virtually populated”– Fast response

● 1 qubit gate

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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● 1200 operations with given parameters

– Possible 2 qubit readout● Different detunings on each allows 4 different cavity

pulls

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Strong coupling experiment● Device:

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Strong coupling experiment● Measurement scheme

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Strong coupling experiment● Qubit parameter determination

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Strong coupling experiment● Vacuum rabi splitting

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Further experiments

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Other quantum bits?

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Stronger couplings?

● Magnetic systems have generally weaker couplings but better coherence– Ensambles can be used to achieve strong

coupling● Done with NV centers

– Coupling can be enhanced by moving closer to the currents

● Superconductors have superficial currents and can allow thinner wires

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Stronger couplings?