1. QUANTUM OPTICS LAB IAP, UNIVERSITÄT BERN Qudit Implementations with Energy-Time Entangled Photons 1 Bänz Bessire Quantum Optics Lab – The Stefanov Group Institute of Applied Physics, University of Bern, Switzerland Quantum Information and Measurement (QIM), Berlin 20.03.2014

2. QUANTUM OPTICS LAB IAP, UNIVERSITÄT BERN 1 20.03.2014Bänz Bessire2 13 Introduction The dit is a -dimensional extension of a classical 2-level system (bit) From a bit to a dit: From a qubit to a qudit: The qudit is a -dimensional extension of a quantum 2-level system (qubit) … … … … … …

3. QUANTUM OPTICS LAB IAP, UNIVERSITÄT BERN 1 20.03.2014Bänz Bessire3 13 Qudit states in quantum information Fundamental tests of quantum mechanics Higher robustness to noise in Bell measurements Larger violation of Bell inequalities D. Collins et al., Phys. Rev. Lett. 88, 032322 (2013) A. Acín, T. Durt, N. Gisin, and J. I. Latorre, Phys. Rev. A 65, 052325 (2002) Quantum key distribution L. Sheridan and V. Scarani, Phys. Rev. A 82, 030301 (2010) Increase secret bit key rate Increase robustness to noise dI d (maximally entangled state) I d (non-maximally entangled state) 22.82 32.872.91 42.903.02 52.913.05 Lower detection efficiencies required for detection loophole free Bell tests T. Vértesi, S. Pironio, and N. Brunner, Phys. Rev. Lett. 104, 060401 (2010)

4. QUANTUM OPTICS LAB IAP, UNIVERSITÄT BERN Polarization entanglement (qubits) P. G. Kwiat et al., Phys. Rev. Lett. 75, 4337–4342 (1995) many more Transverse momentum entanglement (qudits) A. Mair et al., Nature 412, 313-6 (2001) A. Dada et al., Nature Physics 7, 677-680 (2011) M. Agnew et al., Phys. Rev. A 84, 062101 (2011) 1 20.03.2014Bänz Bessire4 13 Photonic entangled qudit states Energy-time (frequency) entanglement (continuous) Discrete time bins (qudits): R. Thew et al., Phys. Rev. Lett. 93, 1–4 (2004) D. Richart et al., Appl. Phys. B 106, 543–550 (2012) Spontaneous parametric down-conversion (SPDC) (idler) (signal) (pump)

5. QUANTUM OPTICS LAB IAP, UNIVERSITÄT BERN 1 20.03.2014Bänz Bessire5 13 Experiment Setup Preparation (SPDC) Manipulation PPKTP Beam dump Detection (SFG) SPCM 5 W pump laser 1064 nm 1 µW 700 s -1 up-converted photons 4-prism compressor: Compensate for dispersion Align the spectrum Spatial light modulator (SLM) Jenoptik S640d 532 nm PPKTP Bandpass filter Complex transfer function: Shaping of the two-photon wavefunction by spectral amplitude and phase modulation with Detected signal after the SFG process: A. Pe’er, B. Dayan, A. A. Friesem, and Y. Silberberg, Phys. Rev. Lett. 94, 073601 (2005) F. Zäh, M. Halder, and T. Feurer, Optics Express 16, 16452-16458 (2008)

6. QUANTUM OPTICS LAB IAP, UNIVERSITÄT BERN 1 20.03.2014Bänz Bessire6 13 Frequency-bin entangled qudits Frequency bins Discretize the SPDC spectrum to obtain entangled qudits Imply a frequency-bin structure with the SLM Independent control Subdivide the spectrum into frequency bins according to

7. QUANTUM OPTICS LAB IAP, UNIVERSITÄT BERN 1 20.03.2014Bänz Bessire7 13 Quantum state tomography C. Bernhard, B. Bessire, T. Feurer, and A. Stefanov, Phys. Rev. A 88, 032322 (2013) Reconstruction of the density matrices for maximally entangled qudits by Maximum Likelihood Estimation Frequency-bin entangled qudits Detected signal is equivalent to the signal of a projective measurement with SLM

8. QUANTUM OPTICS LAB IAP, UNIVERSITÄT BERN By means of projective measurements we determine 1 20.03.2014Bänz Bessire8 13 Frequency-bin entangled qudits 2-qubit / 2-qutrit state with a variable degree of entanglement Collins et al. (CGLMP) introduced a -dimensional Bell parameter Correlations between two separated systems are explainable by a local realistic theory if (CGLMP inequality) Bell measurements D. Collins et al., Phys. Rev. Lett. 88, 040404 (2002) is varied by amplitude modulation with the SLM

9. QUANTUM OPTICS LAB IAP, UNIVERSITÄT BERN 1 20.03.2014Bänz Bessire9 13 Frequency-bin entangled qudits Bell measurement Local detection method (SFG) If non-locality cannot be concluded but entanglement is demonstrated 2-qubit state with a : 2-qutrit state with a : C. Bernhard, B. Bessire, T. Feurer, and A. Stefanov, Phys. Rev. A 88, 032322 (2013) Theory scaled by mixing parameters acc. to A non-maximally entangled qutrit state ( ) violates the CGLMP inequality larger than a maximally entangled qutrit A. Acín, T. Durt, N. Gisin, and J. I. Latorre, Phys. Rev. A 65, 052325 (2002)

10. QUANTUM OPTICS LAB IAP, UNIVERSITÄT BERN 1 20.03.2014Bänz Bessire10 13 Time-bin entangled qudits Time bins with a SLM Analogue to frequency bins we subdivide the time domain into bins Using two time bins corresponds to the Franson concept of 2-photon interferometry SPDC J. D. Franson, PRL 62, 2205 (1989) FT

11. QUANTUM OPTICS LAB IAP, UNIVERSITÄT BERN 1 20.03.2014Bänz Bessire11 13 Time-bin entangled qudits Demonstrate entangled qubits by 2-photon interference Projection of a 2-qubit state onto Finite spectral resolution at SLM plane reduces the visibility Coherence times: SLM B. Bessire, C. Bernhard, T. Feurer, and A. Stefanov, New. J. Phys., 033017 (2014)

12. QUANTUM OPTICS LAB IAP, UNIVERSITÄT BERN 1 Bänz Bessire12 13 Outlook Implementation of other discretization schemes Discretization of the frequency space into Schmidt modes Non-locality measures Use Bell measurement data (qutrit) to calculate the non-local capacity and the distance to the non-local polytope as non-locality measures C. Bernhard, B. Bessire, A. Montina, M. Pfaffhauser, A. Stefanov, and S. Wolf, arXiv:1402.5026 (2014) Improvements of the experimental setup Enhance the detection efficiency by new detection schemes Improved optical resolution Allows for higher dimensions Future projects Two-photon absorption with entangled photons (coherent control) Demonstrate a Kochen-Specker experiment using entangled qutrits (or ququarts) 20.03.2014 B. Bessire, C. Bernhard, T. Feurer, and A. Stefanov, New. J. Phys., 033017 (2014)

13. QUANTUM OPTICS LAB IAP, UNIVERSITÄT BERN 1 Bänz Bessire13 Acknowledgments Thank you for your attention! C. Bernhard S. Lerch S. Schwarz M. Unternährer A. Stefanov T. P. Wihler S. Wolf and his group Collaborators: 20.03.2014 J. Kohn