Adiabatic transfer of light in a double cavity and the optical Landau-Zener problem

Abstract

We analyze the evolution of an electromagnetic field inside a double cavity when the difference in length between the two cavities is changed, e.g. by translating the common mirror. We find that this allows photons to be moved deterministically from one cavity to the other. We are able to obtain the conditions for adiabatic transfer by first mapping the Maxwell wave equation for the electric field onto a Schroedinger-like wave equation, and then using the Landau-Zener result for the transition probability at an avoided crossing. Our analysis reveals that this mapping only rigorously holds when the two cavities are weakly coupled (i.e. in the regime of a highly reflective common mirror), and that, generally speaking, care is required when attempting a hamiltonian description of cavity electrodynamics with time-dependent boundary conditions.

arXiv comment24 pages, 18 figures. Version 2 includes a new section (Sec. VIII) on the regimes of validity of the Schroedinger-like equations and also of the adiabatic approximation, together with a new figure (Fig. 10). The discussion section (Sec. XI) has also been enhanced

References in corpus (37)

• The Quantum Internet
• Circuit Quantum Electrodynamics: Coherent Coupling of a Single Photon to a Cooper Pair Box
• Cavity quantum electrodynamics for superconducting electrical circuits: an architecture for quantum computation
• The Physical Implementation of Quantum Computation
• Quantum state transfer and entanglement distribution among distant nodes in a quantum network
• Strong dispersive coupling of a high finesse cavity to a micromechanical membrane
• Quantum Coherent Atomic Tunneling between Two Trapped Bose-Einstein Condensates
• Strongly Interacting Polaritons in Coupled Arrays of Cavities
• Quantum phase transitions of light
• Coherent dynamics of a flux qubit coupled to a harmonic oscillator
• Strong atom-field coupling for Bose-Einstein condensates in an optical cavity on a chip
• Stopping Light All-Optically
• Cavity QED with a Bose-Einstein condensate
• Distributed quantum computation via optical fibres
• Dispersive optomechanics: a membrane inside a cavity
• Quantum Networking with Optical Fibres
• Reversible state transfer between light and a single trapped atom
• The dynamical Casimir effect in a superconducting coplanar waveguide
• Vacuum Rabi oscillations in a macroscopic superconducting qubit LC oscillator system
• Optics of Nonuniformly Moving Media
• The quantum optical Josephson interferometer
• Photon generation in an electromagnetic cavity with a time-dependent boundary
• Gauge Theories with Cayley-Klein $SO(2;j)$ and $SO(3;j)$ Gauge Groups
• Sonoluminescence as quantum vacuum radiation
• Three level atom optics via the tunneling interaction
• Atom detection and photon production in a scalable, open, optical microcavity
• Quantum Communication with Phantom Photons
• The effect of nonlinearity on adiabatic evolution of light
• Matterwave Transport Without Transit
• The photon shuttle: Landau-Zener-Stueckelberg dynamics in an optomechanical system
• Hybrid apparatus for Bose-Einstein condensation and cavity quantum electrodynamics: Single atom detection in quantum degenerate gases
• Dissipation control in cavity QED with oscillating mode-structures
• Cavity state preparation using adiabatic transfer
• Collapse and revivals of a the photon field in a many-body Landau-Zener process
• Control of atomic decay rates via manipulation of reservoir mode frequencies
• Level crossings in a cavity QED model
• Adiabatic state preparation in a cavity

Cited by in corpus (8)

• Collectively-enhanced optomechanical coupling in periodic arrays of scatterers
• Multiphoton transitions in Josephson-junction qubits (Review Article)
• Enhanced optomechanical readout using optical coalescence
• Catastrophes in non-equilibrium many-particle wave functions: universality and critical scaling
• Dicke-type phase transition in a multimode optomechanical system
• Photon generation and entanglement in a double superconducting cavity
• Parametric amplification of light in a cavity with a moving dielectric membrane: Landau-Zener problem for the Maxwell field
• Emergence of chaos and controlled photon transfer in a cavity-QED network