1. Unusual Interferometry via Translational-Internal Entanglement Nir Bar-Gill Michal Kolar Tomas Opatrny Gershon Kurizki

2. Outline  Interferometry Which-way and phase information  Disorder Momentum localization

3. Interferometric Information  Use a TIE particle in a Mach-Zehnder interferometer  Compared to standard particles Information stored in 4D Hilbert space Both which-way and phase information can be extracted

4.  Insert a which way detector with distinguishability D  The state in the interferometer is measured  The probability to reach the output detectors  Thus, the visibility of the interference pattern is, and thus Standard MZI with which-way detector a reminder D

5.  Initial state:  No which-way detector  Phases of internal states acquired according to path length (due to entanglement with different momentum states)  WW marker travels with the particle Interferometer for Translationally- Internally Entangled Particles TIE with birefringent photons / two-level atoms

6.  Mean path lengths L A,L B are known  We choose internal state projection basis at output accordingly  The click probability at the detectors following an  projection:  The interference pattern is Output Detectors ( Click: A  B)

7. TIE Interferometry  Visibility not good measure (interference pattern not sinusoidal)  Phase sensitivity:  Standard case: S max =V S 2 +D 2  1  TIE case (e.g. k 1 /k 2 =3): S =1/3, D  1 S 2 +D 2 >1 D TIE TIE Interference Standard Interference

8.  Couple random momentum states of an atom using resonant two-photon processes  Create diagonal order or disorder using TIE Order: Disorder: random k i → Momentum Localization using TIE atom Coupling beams (regular or random angles)

9. Hamiltonian of Random Momenta  Hamiltonian with random diagonal elements, and controllable coupling strengths  Through the change of coupling strength J, we can access the weak disorder regime - Strong disorder regime -

10. Localization via Multi-State Coupling  Due to coupling between ground state and all other states – N-dimensional system Localization occurs for certain (finite)

11. Interference Fringe Visibility: Measure of momentum localization  Passing the atom through an interferometer (light grating) can measure momentum distribution

12. Conclusion  Interferometry TIE gives both which-path and phase information Does not obey standard complementarity  Momentum Localization via TIE “ Anderson-like ” disorder in momentum space Strength of disorder controlled by strength of interactions Localization measured through TOF images or visibility of interference pattern

13. The End