Open Quantum Systems

Transcription

1 Open Quantum Systems

2 Basics of Cavity QED There are two competing rates: the atom in the excited state coherently emitting a photon into the cavity and the atom emitting incoherently in free space

3 Basics of Cavity QED To Detector Free Space κ Cavity (Photons) Atom There are two competing rates: the atom in the excited state coherently emitting a photon into the cavity and the atom emitting incoherently in free space

4 Open Quantum Systems system Reservoir or Bath In reality, the system is not isolated but coupled to a reservoir (characterized by many degrees of freedom or many particles or modes)

5 Open Quantum Systems system Reservoir The system, the reservoir and their (little) interaction can all be described by interaction energies or Hamiltonians

6 Open Quantum Systems system Reservoir So solve the larger system! But that is much harder and anyways we are usually interested only in the system behavior.

7 Density Matrix: In general: Open Quantum Systems system Reservoir For pure states: Operator expectation value: Try to get an effective equation for the system

8 Open Quantum Systems Density Matrix: Evolution: system Reservoir System and Environment: System: Try to get an effective equation for the system

9 Master Equation system Reservoir To take the trace on the R.H.S one needs to approximate the reservoir to a point that it becomes a mere spectator: Born approximation: The reservoir is so large that it remains unaffected by the system Markov approximation: The reservoir has no memory of the past.

10 Master Equation system Reservoir For atoms: For cavities:

11 Master Equation: Criticism system Reservoir All degrees of freedom of the reservoir are integrated out. No information is left in the reservoir. It is hard to develop physical intuition with density matrix! Computationally costly: N^2-1 elements as opposed to n elements Atom-Photon Interactions Cohen-Tanoudjii

12 Stochastic Wave-function approach system Reservoir Jump Operator that changes the state Develop an effective wave-function approach from the master equation Carmichael: An open systems approach to Quantum Optics and Lecture Notes, Dalibard, Castin, Molmer :

13 Stochastic Wave-function approach system Reservoir Lesson: As long as the quantum jump probabilities are small, one can effectively use a non-hermitian Hamiltonian with a wave-function to describe the dynamics.

14 Atoms in cavity: Vacuum Rabi Splitting Infact, the primary aim of experimental design for cavity QED is also to satisfy this condition: to observe coherent atom-photon dynamics

15 Strong coupling condition

16 Atoms in cavity Adiabatically following the ground state manifold κ

17 Eliminating the excited state (EIT)

18 Eliminating the excited state (EIT) The Dark State is completely decoupled from the excited state: No spontaneously sca.ered photons

19 Atoms in cavity Either choose a vary good cavity (Harcoche et. al.) Adiabatically following the ground state manifold Or terminate the process, when a photon is detected: Quantum Feedback κ

20 Feedback!me The process is terminated at the instance a photon is detected out of the cavity

21 Atoms in cavity: Vacuum Rabi Splitting Diagonalize in the manifold: and Line-width of the splitting The energy spectrum is split and the splitting persist even for no photons!

22 When can one see this? Strong coupling condition Strong condition: Weaker condition:

23 Larmor Precession of atoms in cavity Time B Phys. Rev. Le-.,103,043601(2009).. Frequency

24 Strong coupling: Single atom co-operativity Single atom cooperativity: Universality: Independent of any details of the atoms:

25 Physical Systems

26 Optical cavity Two mirrors with high reflectivity placed a distance L apart Photo Source: G. Rempe group, Max planck, Germany

27 How a cavity looks like Laser cooled atoms

28 Atoms in cavity Video: Thanks to Kimble Lab. Photo Source: Nature 424, 839, 2003

29 Systems Trapped ions Quantum dots Defect centers Super-conducting Qubits And several others

30 Applications Exploring the Quantum: Atoms, Cavities and Photons Haroche and Raimond

31 Collapse and Revival Phys. Rev. Le-.,94, (2009)..

32 SuperconducSng qubit C Josephson tunnel juncsons L J 100 µm

33 Quantum jumps Quantum jumps due to spontaneous decay R. Vijay, D.H. Slichter, and I. Siddiqi (Phys. Rev. Le[. 106, (2011))

34 Transferring a photon from one atom to another via a cavity Measured visibility of 88 % Nature Physics, 3, 765, (2007). Nature, 449, 438 (2007). Nature, 499, 443 (2007).

35 Seeing Photons ChrisSne Guerlin, Julien Bernu, Samuel Dele glise, Cle ment Sayrin, Se bassen Gleyzes, Stefan Kuhr, Michel Brune, Jean- Michel Raimond and Serge Haroche, Nature, 448, 889 (2007)

36 Physics Nobel Serge Haroche College de France, Paris Dave Wineland NIST and JILA, Boulder, Colorado The Nobel Prize in Physics 2012 was awarded jointly to Serge Haroche and David J. Wineland "for ground- breaking experimental methods that enable measuring and manipula!on of individual quantum systems Informa!on: h-p://

37 Quantum Network Material systems form nodes Single photon channels connect the nodes Motivation : Quantum cryptography, computation and simulations

38 Quantum Network Agenda: Store and retrieve single photons Entangled nodes Unitary operations

39 Cavity QED: a quantum node