Prospect of using single photons propagating through Rydberg EIT medium for quantum computation

1. Ashok Mohapatra National Institute of Science Education and Research, Bhubaneswar Prospect of using single photons propagating through Rydberg EIT medium for quantum computation

2. Outline • Introduction to quantum computation using photons • Introduction to Rydberg EIT and its non-linearity • Our experimental progress at NISER • Conclusion

3. Classical computer Quantum computer Bit Qubit 0 V or 5 V of a transistor output 2-level quantum system (e.g. Single photon) Polarization states: |H> or |V> |> = 1|H> + 2 |V> 0 or 1 |α1|2+|α2|2=1 Classical gates AND, OR, NOT etc (Universal) Single qubit rotation operators and 2-qubit Controlled-NOT gate (Universal quantum gates)

4. Qunatum computation using photons • Single photon source • Single photon detctors • Optical elements for gate operation • A Kerr non-linear medium for interactions of photons to devise a CNOT gate

5. Single qubit quantum gates • Each photon as a qubit with two orthogonal polarized state Quarter wave plate Hadamard gate Half wave plate two Hadamard operation

6. CNOT gate:Interaction of photons Kerr non-linearity of a medium Increasing the length doesn‘t help due to strong absorption in the medium Electromagnetically Induced Transparency (EIT) provides a larger 3rd order non-linearity without absorption. where n2 ≈ 10-20 m2/W for typical glass

7. Electromagnetically induced transparency (EIT) nS1/2 6 MHz 5P3/2 F‘=3 Probe (Ωp) F=2 5S1/2 F=1 87Rubidium

8. Electromagnetically induced transparency (EIT) nS1/2 σ- Coupling (Ωc) 6 MHz 5P3/2 F‘=3 500 kHz σ+ Probe (Ωp) F=2 5S1/2 F=1 87Rubidium EIT still doesn‘t provide enough non-linearity at single photon level

9. Rydberg EIT Rydberg state nS1/2 σ- Coupling (Ωc) 6 MHz 5P3/2 F‘=3 500 kHz σ+ Probe (Ωp) F=2 5S1/2 F=1 87Rubidium Rydberg EIT: Mohapatra et al., PRL, 98, 113003 (2007) (Thermal atoms) Weatherill et al., J. Phys. B, 41, 201002 (2008) (Cold atoms)

10. Rydberg atoms Rydberg states: large n Scaling with principal quantum number n (low) Few 100 nm Size n2 Dipole moment n2 Lifetime n3 Polarizability n7 van der Waals n11 Strong dipolar interaction Long lived 100 μsec for n > 40 5P3/2 5P1/2 Giant Kerr effect Sensitivity to electric fields Strongly interacting (QIP) Atom - atom interactions 5S1/2

11. Rydberg Rydberg interaction Simplest case: van der Waals E Ω Atomic distance

12. Rydberg blockade Simplest case: van der Waals E Ω blockade condition Atomic distance fewµm

13. Rydberg blockade Ω ≡ Urban et al., Nature Phys. 5, 110 (2009) Gaetan et al., Nature Phys. 5, 115 (2009) Wilk et al., Phys. Rev. Lett. 104, 010502 (2010)

14. Superatom Vogt et al., PRL 97, 083003 (2006) Heidemann et al., PRL 99, 163601 (2007) Raitzsch et al., PRL 100, 013002 (2008)

15. Non-linearity of Rydberg EIT Rydberg state Coupling (Ωc) 6 MHz 500 kHz Probe (Ωp) F=1 Dark state that doesn‘t couple to the probe beam and hence probe beam become transparent

16. Non-linearity of Rydberg EIT In the blockade sphere, more than one atom can not be excited which makes the dark state very fragile and get mixed with intermediate state. For large probe power, the EIT peak reduces with larger probe absorption. • One, (b) two, (c) three atoms per • blockade sphere Durham university, UK group Pritchard et al. PRL, 105, 193603 (2010)

17. Non-linearity of Rydberg EIT(Pushing to single photon level) MIT group Peyronel et al. Nature, 488, 57 (2012)

18. Non-linearity of Rydberg EIT(Pushing to single photon level) MIT group, 2013, Firstenberg et al. www.nature.com/doifinder/10.1038/nature12512

19. Optical non-linearity of Rydberg EITin thermal vapor • Rydberg blockade radius is only scaled approximately by a factor of 3 in thermal vapor • Kuebler et al. Nature Photo. 4, 112 (2010) • Optical pumping rate to the dark state is much faster than the transit time of the atoms

20. Measurement of the non-linear refractive index Rydberg EIT medium ω ω+δ

21. Measurement of the non-linear refractive index Rydberg EIT medium ω ω+δ

22. Measurement of the non-linear refractive index Rydberg EIT medium 5s1/2(F=3)→5p3/2(F’)→45d 5s1/2(F=3)→5p3/2(F’)→44s 5s1/2(F=3)→5p3/2(F’)→49d

23. Acknoledgement Arup Bhowmik (PhD) Sabyasachi Barik (Int. MSc) Surya Narayan Sahoo (Int. MSc) Charles Adams group at Durham University

24. Thank You

25. Rydberg EIT with large probe power

26. EIT with large probe power

27. Rydberg EIT in thermal vapor

28. Rydberg EIT in thermal vapor

29. 44d EIT spectra Reference: Mohapatra et al. PRL (2007)

30. High precession spectroscopy (d - state fine structure splitting) Mohapatra et al. PRL 98, 113003 (2007). K. C. Harvey et al, Phys. Rev. Lett. 38, 537 (1977). W. Li, I. Mourachko, M. W. Noel, and T. F. Gallagher, Phys. Rev. A 67, 052502 (2003).

31. Giant Kerr effect of Rydberg EIT medium ns 5p 5s Electric field sensitivity of Rydberg state combined with the non-linear properties of EIT

32. Giant Kerr effect of Rydberg EIT medium ΔW ns 5p 5s Electric field sensitivity of Rydberg state combined with the non-linear properties of EIT • ∆W: • Stark shift by applying an external Electric field (DC Kerr effect) • Interaction induced shift (Similar to AC Kerr effect) (DC Kerr effect)

33. Experimental demonstration by phase modulation of light Spectrum analyzer Fast photodetector (1.2 GHz bandwidth) + - AOM

34. Phase modulation of light (Sideband spectra)

35. Phase modulation of light (Sideband spectra)

36. N-dependence of the Kerr constant α scales as n*7 Ωc scales as n*-3/2 c1 determines the absolute maximum c2 determines the n* dependent scaling

37. Kerr effect in Rydberg EIT medium(Order of magnitude calculation) Gas (CO2, 1 atm) B0≈ 10-18 m/V2 Water B0≈ 10-16 m/V2 Glass B0≈ 10-14 m/V2 Nitrobenzene B0≈ 10-12 m/V2 Rydber dark state (thermal atoms) B0≈ 10-6 m/V2 6 orders of magnitude bigger 10 orders of magnitude is expected for cold atoms

38. Noise spectra Spectrum analyzer AOM

39. More on Electro-optic and electrometry • Electro-optic control of Rydberg dark state polariton Bason et al. PRA 77, 032305 (2008) • Enhanced electric field sensitivity of rf-dressed Rydberg dark states (Bason et al. Bason et al. New J. Phys. 12, 065015 (2010)

40. Outlook • QIP using thermal atoms in microcell • Quantum computation using photon • Single photon source • Quantum computation using mesoscopic ensemble of atoms • Versatile electric field sensor • THz imaging

41. THz imaging Replace the EO crystal by Rydberg EIT in a microcell filled with thermal atoms (Preliminary idea)

42. Durham University Group Prof. C. S. Adams Dr. K. J. Weatherill Mr. M. G. Bason Mr. J. Pritchard Mr. R. Abel

43. Thank You

44. Frequency stabilization of blue laser to a EIT peak using frequency modulation scheme (schematic) EOM λ/4 λ/4 Di-chroic mirror λ/2 λ/2 30 dBm power amplifier Photodetector 1 MV/W, 10 MHz Toptica SHG @ 480 nm 20 dB amplifier Mixer Phase shifter Slow feedback to master piezo ECDL @ 780 nm Toptica DL pro LP filter Stabilized to Polarization spectroscopy PID Fast feedback to master current (BW ~ 1 MHz) Toptica FALC module

45. Home made EOM D. J. McCarron et al., Meas. Sci. Tech. 2008

46. Frequency stabilization of blue laser to a EIT peak using frequency modulation scheme Ultra-stable, no long term drift and 100 kHz of relative line-width observed with 1 μW of probe power Stabilization demonstrated for 26D5/2 state by using less than 2 mW of blue light For 58D3/2 state, less than 15 mW of blue light was used Abel et al, under preparation

47. Kerr effect in Rydberg EIT medium

48. Kerr effect in Rydberg EIT medium In the regime

49. Kerr effect in Rydberg EIT medium In the regime

50. Kerr effect in Rydberg EIT medium In the regime Kerr effect (1875)