Christine Muschik and J. Ignacio Cirac Entanglement generated by Dissipation Max-Planck-Institut für Quantenoptik Hanna Krauter, Kasper Jensen, Jonas Meyer Petersen and Eugene Polzik Niels Bohr Institute, Danish Research Foundation Center for Quantum Optics (QUANTOP)

Steady State Entanglement

Motivation: Quantum entanglement Basic ingredient in most applications in the field of quantum information But: Lifetimes are usually very short Therefore: Need for much longer lifetimes!

Motivation: Quantum entanglement Basic ingredient in most applications in the field of quantum information But: Lifetimes are usually very short Therefore: Need for much longer lifetimes! Typically: Quantum states are fragile under decoherence

Motivation: Quantum entanglement Basic ingredient in most applications in the field of quantum information But: Lifetimes are usually very short Therefore: Need for much longer lifetimes! Typically: Quantum states are fragile under decoherence Avoidance of dissipation by decoupling the system from the environment

Motivation: Quantum entanglement Basic ingredient in most applications in the field of quantum information But: Lifetimes are usually very short Therefore: Need for much longer lifetimes! Typically: Quantum states are fragile under decoherence Avoidance of dissipation by decoupling the system from the environment Strict isolation!

Motivation:

New approaches Use the interaction of the system with the environment

Motivation: New approaches Use the interaction of the system with the environment Dissipation drives the system into the desired state

Motivation: New approaches Use the interaction of the system with the environment Dissipation drives the system into the desired state Robust method to create extremely long-lived and robust entanglement

Motivation: Procedure:

Motivation: Procedure: Engineer the coupling

Motivation: Procedure: Engineer the coupling Steady state = desired state

Motivation: Procedure: Engineer the coupling Steady state = desired state Arbitrary initial state

Motivation: Procedure: Engineer the coupling Steady state = desired state Arbitrary initial state

Motivation: Procedure: Engineer the coupling Steady state = desired state Arbitrary initial state Single trapped ion J. F. Poyatos, J. I. Cirac and P. Zoller, Phys. Rev. Lett. 77, 4728 (1996) Atoms in two cavities B. Kraus and J. I. Cirac, Phys. Rev. Lett. 92, (2004) Many-body systems S. Diehl, A. Micheli, A. Kantian, B. Kraus, H.P. Büchler, P. Zoller, Nature Physics 4, 878 (2008) F. Verstraete, M.M. Wolf, J.I. Cirac, Nature Physics 5, 633 (2009) Proposals: Quantum phase transitions State preparation Quantum computing

Motivation: Procedure: Engineer the coupling Steady state = desired state Arbitrary initial state

Setup:

Main idea: Hamiltonian:

Main idea: Hamiltonian: Master equation:

Main idea: Hamiltonian: Master equation: Unique Steady State:

Setup: laser magnetic fields

Setup: Reservoir: common modes of the electromagnetic field. Control: Laser and magnetic fields laser magnetic fields

Setup: laser

Setup: laser

Setup: laser

Setup: laser

Setup: laser

+undesired processes Masterequation: Entanglement: Theory:

Entanglement: ideal case Theory:

Entanglement: ideal case : polarization : noise rate Entanglement: including undesired processes Theory:

Experimental realization of purely dissipation based entanglement: Theory: Two-level model Experiment: Multi-level structure

Experimental realization of purely dissipation based entanglement: Theory: Two-level model Experiment: Multi-level structure (nuclear spin I=7/2)

Experimental results:

EPR variance

Experimental results: Longitudinal spin EPR variance

Experimental results:

Conclusions and Outlook: First observation of entanglement generated by dissipation

Conclusions and Outlook: First observation of entanglement generated by dissipation Entanglement was produced with macroscopic atomic ensembles, and lasted much longer than in previous experiments where entanglement was generated using standard methods.

Conclusions and Outlook: First observation of entanglement generated by dissipation Entanglement was produced with macroscopic atomic ensembles, and lasted much longer than in previous experiments where entanglement was generated using standard methods. This work paves the way towards the creation of long lived entanglement, potentially lasting for several minutes or longer.

Conclusions and Outlook: Realization of Steady State Entanglement: Atoms with two-level atomic ground states, e.g. Yb 171

Conclusions and Outlook: Realization of Steady State Entanglement: Atoms with two-level atomic ground states, e.g. Yb 171 Increased optical depth + optical pumping

Conclusions and Outlook: Realization of Steady State Entanglement: Atoms with two-level atomic ground states, e.g. Yb 171 Increased optical depth + optical pumping Reduced spin-flip collisions Better coatings, lower temperatures

Proposal for long-lived entanglement Other systems, e.g. optomechanical oscillators Summary: Dissipatively driven entanglement Future General theoretical model for quadratic Hamiltonians

Main idea: Steady state:

Effective ground state Hamiltonian: Master equation: Entanglement: