1 / 20

Entanglement of indistinguishable particles

Entanglement of indistinguishable particles. Libby Heaney Paraty Workshop, 2009. Particle entanglement. Entanglement usually considered between degrees of freedom of two or more well separated quantum systems. Hilbert space has a tensor product structure.

troy-hays
Télécharger la présentation

Entanglement of indistinguishable particles

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Entanglement of indistinguishable particles Libby Heaney Paraty Workshop, 2009

  2. Particle entanglement • Entanglement usually considered between degrees of freedom of two or more well separated quantum systems. • Hilbert space has a tensor product structure. • Entanglement is assigned to the state alone. Entanglement of indistinguishable particles

  3. Indistinguishable particles • Identical particles whose wavefunctions overlap in space. • Hilbert space no longer has the tensor product structure required to correctly define entanglement. • Cannot assign to either particle a specific set of degrees of freedom. Anti-symmetrised state of two fermions P. Zanardi, PRA 65 042101 (2002) Entanglement of indistinguishable particles

  4. Entanglement of indistinguishable particles • Two methods for defining entanglement of indistinguishable particles: • Include detection process in the definition of particle entanglement. Tichy, et al. arXiv:0902.1684v3. • Use the formalism of second quantisation and consider entanglement of modes. e.g. P. Zanardi, PRA 65 042101 (2002), Ch. Simon, PRA 66052323 (2002), … J. Goold, et al. PRA 80 022338 (2009). • Is mode entanglement as genuine as particle entanglement? LH and V. Vedral, arXiv:0907.5404v1. Entanglement of indistinguishable particles

  5. ENTANGLEMENT OF IDENTICAL PARTICLES AND THE DETECTION PROCESS Entanglement of indistinguishable particles

  6. Entanglement of identical particles • Assign identity to particles by including the detection process. • A priori entanglement of the state is the distinguishable particle entanglement. • Physical entanglement – apply an entanglement measure to the above state. • Note for indistinguishable particles there is a non-zero probability of detecting both particles in the same region of space. Tichy, de Melo, Kus, Mintert and Buchleitner, arXiv:0902.1684v3 Entanglement of indistinguishable particles

  7. Entanglement of indistinguishable particles Indistinguishable distinguishable distinguishable indistinguishable Entanglement of indistinguishable particles

  8. MODE ENTANGLEMENT Entanglement of indistinguishable particles

  9. Mode entanglement • Another approach to define entanglement of indistingiushable particles is to move into second quantisation formalism. • Energy modes • Spatial modes • Entanglement may exist between modes occupied by particles. Entanglement of indistinguishable particles

  10. Simple example of mode entanglement • Entanglement between two spatial modes occupied by a single particles. • In second quantisation: 1st quantisation: Superposition of A and B. 2nd quantisation: Entanglement of A and B. Entanglement of indistinguishable particles

  11. Is mode entanglement genuine entanglement? • For photons it is generally accepted that mode entanglement is as genuine as particle entanglement. • Tan et al PRL 66 252 (1991). • Hessmo et al, PRL 92 180401 (2004). • Van Enk, PRA 72 064306 (2006). • No experiments have tested mode entanglement of massive particles. • Disputed whether mode entanglement of massive particles is genuine, due to a particle number superselection rule. Entanglement of indistinguishable particles

  12. A B Particle number superselection rule • Since the correlations of entanglement are basis independent, to verify entanglement requires measurements in at least two bases. • For mode entanglement, one measurement setting could be the particle number basis, but what about another measurement setting? Implies creation or destruction of particles: is forbidden for an isolated system. Entanglement of indistinguishable particles

  13. Overcoming the particle number superselection rule • Locally overcome the particle number superselection rule by exchanging particles with a particle reservoir. • Eg. Dowling et al. Phys. Rev. A, 74, 052113 (2006), see also Bartlett, et al., Rev. Mod. Phys. 79 555 (2007). • LH and J. Anders, PRA 80 032104 (2009), S.-W. Lee, LH andD. Jaksch, In preparation. Entanglement of indistinguishable particles

  14. MODE ENTANGLEMENT OF MASSIVE PARTICLES IS USEFUL FOR QUANTUM COMMUNICATION Entanglement of indistinguishable particles

  15. Dense coding protocol Classically, i.e. with bits, one can send 2 messages per use of the channel, C=1. Quantum mechanically, i.e. with qubits (and by utilizing entanglement), one can send 4 messages per use of the channel, C=2. • System: Maximally entangled Bell state. • Encoding: Alice acts on her qubit to encode one of four messages. • Alice sends her qubit to Bob. • Decoding: Bob performs Bell state analysis to recover which of the four messages Bob transmitted. Entanglement of indistinguishable particles

  16. Dense coding with mode entanglement • System – double well formed of tightly confined potentials: • A single particle is initialised in the state: LH and V. Vedral, arXiv:0907.5404v1 Entanglement of indistinguishable particles

  17. Dense coding with mode entanglement • Encoding (X and Z operations on mode A): • Here no coupling between modes (J=0) – Alice acts solely on her mode. • Z operation: • X operation: Shared BEC reservoir: Apply a potential bias to mode A. Entanglement of indistinguishable particles

  18. Dense coding with mode entanglement • Exchange of particles between the BEC and mode B. • Interaction between modes: Drive bosons to the hardcore limit - they behave like Fermions. Allow tunneling so that the particles exchange positions. • Couple both modes to BEC to rotate to the particle number basis (eliminates the BEC phase). • Read out: The four outcomes, • |00>, |01>, |10> and |11> • correspond to the four Bell states. • Alice sends her mode to Bob. • Decoding (Bob performs complete Bell state analysis on both modes): Entanglement of indistinguishable particles

  19. Summary • Entanglement between the degrees of freedoms of indistinguishable particles is meaningful if one takes the detection process into account. • Indistinguishability can even generate entanglement between particles that have no a priori entanglement. • A tensor product Hilbert space is recovered by considering entanglement of modes occupied by particles. • The particle number superselection rule can be locally overcome by coupling to a reservoir Bose-Einstein condensate. • Mode entanglement of massive particles can, in principle, be used as a resource for quantum communication. Entanglement of indistinguishable particles

  20. THANK YOU FOR LISTENINGANY QUESTIONS? Entanglement of indistinguishable particles

More Related