Experimental Demonstration of Spinor Slow Light Ite A. Yu Department of Physics Frontier Research Center on Fundamental & Applied Sciences of Matters National Tsing Hua University Taiwan
Motivation Quantum information wave function. Photons: ultimate speed, inert to the environment, no collision with each other Ideal carriers for quantum information. One qubit = single photon, so qubit-qubit operation or photon-photon interaction: nonlinear optical process. Nonlinear efficiency = (transition rate) (interaction time), but transition rate light intensity and is usually very low at single-photon level (10 W 10 20 photons/second). Slowing or stopping light can greatly enhance the interaction time A sufficient nonlinear efficiency can be achieved even at single-photon level.
Experimental setup Outline Electromagnetically induced transparency, slow light & stopped light Quantum memory & low-light-level nonlinear optics Double tripod (DT) scheme & two-component or spinor slow light (SSL) Oscillation between the two components & the SSL interferometer SSL qubits and DT scheme as quantum memory/rotator Conclusion
Quadrupole Magnet PD PD T Experimental System of Cold Atoms T z T T T y T Coupling Laser Probe Laser 5P 3/2 F' = 3 Trapping F = 2 We produce 10 9 atoms 87 Rb with a temperature of 300 K with a magnetooptical trap (MOT). Coherence time ( coh ) ~ 100 s & optical density (OD) ~ 200, where OD is defined by I out = I in e -OD. x T: trapping laser beams Quadrupole Magnet 2 1 0 5S 1/2 1 Repumping Coupling Probe
NTHU Optical Jungle 8 diode lasers; MOPA; UHV system; > 300 optical components simple physics system; complicate experimental setup
Magneto-Optical Trap 1 1mm 0 Dimension: 9.21.81.8 mm 3
The Phenomenon of Electromagnetically Induced Transparency (EIT) Probe 1 3 probe laser atoms Large Optical Density (OD) Transmission = e -200 10-87!!! 3 Probe Coupling probe laser atoms Transmission 1 coupling laser 1 2
Narrow and High-Contrast EIT Spectrum Y. F. Chen, Y. C. Liu, Z. H. Tsai, S. H. Wang, & IAY, PRA 72, 033812 (2005). << 3 OD = 7 Probe 1 Coupling 2 Near the resonance, OD = 7 and probe transmission is e -7 (less than 0.1%). Transmission is nearly 100% at the resonance and the transparency window is much narrower than the natural linewidth,. Narrow & high-contrast absorption profile. => large dispersion => slow group velocity.
Narrow and High-Contrast EIT Spectrum Y. F. Chen, Y. C. Liu, Z. H. Tsai, S. H. Wang, & IAY, PRA C. C. 72, Lin, 033812 M. C. Wu, (2005). B. W. Shiau, Y. H. Chen, IAY, Y. F. Chen, & Y. C. Chen, PRA 86, 063836 (2012). << 3 Transmission10% OD = 7 @ detuning=5 Probe 1 Coupling 2 e -228 10-99 Near the resonance, OD = 7 and probe transmission is e -7 (less than 0.1%). Transmission is nearly 100% at the resonance and the transparency window is much narrower than the natural linewidth,. Narrow & high-contrast absorption profile. => large dispersion => slow group velocity.
Probe Transmission 1.0 0.5 0.0 1.0 0.5 Input Pulse Slow Light and Stopped Light Storage Time ~ 4 s Coupling Field Delay Time ~ 3.5 s Output Pulse in = 1.24s OD = 147 c = 1.15 = 5.5*10-4 QE = 69% 0.0 0 2 4 6 8 10 12 14 Time (s) In the constant presence of the coupling, speed of the light pulse c/10 5. The 1 km-long probe pulse is compressed to 1 cm inside the atoms. The gap of ~ 4 s in the probe signal demonstrates the light storage.
3 Coherent Storage for Photons 3 Input Probe Writing Coupling Output Probe Reading Coupling 1 two-photon Raman transition 2 1 2 1 atomic wave function: ground-state (Raman) coherence or spin excitation The EIT storage is a coherent process and provides a method for exchange of wave functions between photons and atoms. 2 reversed two-photon Raman transition
High Storage Efficiency and Large Delay-Bandwidth Product Y. H. Chen, M. J. Lee, I. C. Wang, S. Du, Y. F. Chen, Y. C. Chen, & IAY, PRL 110, 083601 (2013). SE E out E in DBP t storage t pulse Fidelity 2 ψ out ψ in ψ in ψ in ψ out ψ out (a) Beat-Note Interferometer Data Reference Read-out Write-in DBP = 74 (b) (c) Time (s) Optimal pulse shape & backward retrieval to enhance SE. 100 ns We report a EIT memory with storage efficiency of 78%, delay-bandwidth product of 74 at SE = 50%, and fidelity 0.9.
Probe p Low-Light-Level Nonlinear Optics Cross-Phase Modulation (XPM) based on Stored Light Y. F. Chen, C. Y. Wang, S. H. Wang, & IAY, PRL 96, 043603 (2006). Storage Writing c Signal 4 3 2 Ground-State Coherence 1 Phase Modulation Probe p Retrieval The stored ground-state coherence is equivalent to the probe pulse. Reading c Single-photon XPM or AOS: quantum phase gates, entangled photon pairs, quantum nondemolition measurements. XPM: a phase shift of 44 is obtained at 18 photons per atomic absorption cross section. How to further improve?
Probe p Low-Light-Level Nonlinear Optics Cross-Phase Modulation (XPM) based on Stored Light Y. F. Chen, C. Y. Wang, S. H. Wang, & IAY, PRL 96, 043603 (2006). Storage Writing c All-Optical Switching (AOS) = 0 Signal 4 3 2 Ground-State Coherence 1 Amplitude Phase Modulation Probe p Retrieval The stored ground-state coherence is equivalent to the probe pulse. Reading c Single-photon XPM or AOS: quantum phase gates, entangled photon pairs, quantum nondemolition measurements. XPM: a phase shift of 44 is obtained at 18 photons per atomic absorption cross section. How to further improve?
Remaining Energy (arb. units) ) All-Optical Switching with Stopped Light Pulses Y. W. Lin, W. T. Liao, T. Peters, H. C. Chou, J. S. Wang, H. W. Cho, P. C. Kuan, & IAY, PRL 102, 213601 (2009). Y. H. Chen, M.J. Lee, W. Hung, Y. C. Chen, Y. F. Chen, & IAY, PRL 108, 173603 (2012). 0.5 (b) 0.4 0.3 0.2 0.1 1.0 0.8 0.6 two moving pulses 0.4 0.2 0.0 0.0 50 0 70 20 4090 60 110 80 130 100 D2 Switching Ratio = exp[(n/a)] SLP Duration (s) 0 1 2 3 4 5 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 (b) two stopped pulses 40 60 80 100 120 OD D2 OD D1 / ( c ) 2 The interaction time can be, in principle, as long as possible. With stopped light pulses, 1.8 or the switch was achieved at 0.56 photons per atomic absorption cross section 4-fold improvement.
Nature Physics, April 2012, p. 252. Stopping light pulses and making them interact in a medium is a way to get more for less. Frozen light switch Frozen light switch
Summary of EIT, Slow Light and Stopped Light 3.5 Acknowledgments for collaborators: Prof. 2.5Yong-Fan Chen (PHYS, NCKU) SLP (s) Remaining Energy (arb. units) 3.0 2.0 1.0 Dr. Ying-Cheng Chen (IAMS, AS) 1.5 1.0 (a) 0.4 The 0.5 EIT/slow light effect 0.2 enhances the 0.0 0.0 light-matter interaction and achieves D2 significant nonlinear optical efficiency even at single-photon level. 30 50 70 90 110 130 EIT-based storage of light transfers quantum states between photons and atoms, making quantum memory feasible. 0.8 0.6 SLP Duration (s) 0 1 2 3 4 5 40 60 80 100 120 However, previous experiments all dealt with single-component slow light. 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 (b) OD D2
Acknowledgments $$$ MOST $$$ $$$ NTHU Top-Notch $$$ Neil HWC MJL GJ KFC Collaboration Projects: Taiwan-Latvia-Lithuania & EU FP7 COLIMA Experiment: Nat l Tsing Hua U. Dr. Meng-Jung Lee Neil Lee Kao-Fang Chang Dr. Hung-Wen Cho Theory: Vilnius U. Gediminas Juzeliūnas Julius Ruseckas Viačeslav Kudriašov
Double Tripod System Three atomic ground states coupled to two excited states by 4 coupling fields A1, A2, B1 & B2 and 2 probe fields A & B. Spinor (Two-Component) Slow Light B B A 2 DT Two Coupled EITs A B A B 2 B1 A B2 A1 A2 1 0 2 A1 = A2 = B1 = B2, ε A,out ε = e (2φ2 /OD) cos φ sin φ B,out sin φ cos φ 1 0 0 2 ε A,in 1 0 δ ε, φ = OD Γ B,in 2Ω 2
Transition Scheme 780nm B 5P 3/2,F= 2,m=1 A 5P 1/2,F= 2,m=1 6.8 GHz 795nm B2 A2 B1 A1 1 δ 5S 1/2,F=2,m=0 2 5S 1/2,F=1,m=0 δ A B 0 5S 1/2,F=2,m=2 Optically pump all population to a single Zeeman state A simple 5-level DT system. of the probe field A and the coupling fields A1 & A2 is ~ 795 nm. of the probe field B and the coupling fields B1 & B2 is ~ 780 nm.
Experimental Scheme Adjust the position of a prism to make four coupling fields in phase. Overlap all coupling fields as they interact with the atoms.
Energy Transmission 0.8 Oscillation between the Two Components ε A,out Output probe A (red) & probe B (blue) as functions of detuning: ε A,out 2 ε = e (2φ2 /OD) cos φ sin φ B,out 2 = e (4φ2 /OD) cos 2 φ ε sin φ cos φ B,out sin 2 φ, where φ = OD Γ 2Ω 2. = 0 1 0, 0.6 0.4 /(2) = -160 khz 0.2 0.0-600 -400-200 0 200 400 600 (khz) /(2) (khz)
ε A,out Stored Spinor Slow Light ε = e (2φ2 /OD) cos φ sin φ B,out sin φ cos φ 1 0, where φ = OD Γ 2Ω 2. OD Γ/(2 2 ) is the delay time of slow light propagation, i.e. φ = d. Can d be replaced by s (storage time)? s = 15 s Large phase change & little decay Phase-sensitive detector or interferometer /(2) (khz)
Interferometer based on Stored Spinor Slow Light B1 A1 A A B B A B2 B2 A2 1 0 2 A storage time ~ O(100s) results in a precision ~ O(100Hz). The SSL interferometer can be used to detect two-photon detuning, Zeeman shift, AC Stark shift, etc. φ = s : fix and vary s (the storage time). Set 1 /(2) = 10.0 khz Set 2 /(2) = 20.0 khz Measured 2-1 = 9.7 khz
SSL as a Two-Color Qubit = 1 A, 0 B + 0 A, 1 B Single-photon SSL is a qubit with the superposition state of two frequency modes. (,) = (cos, sin) and where φ = s. In long-distance quantum communication, photons of two-color quantum states are inert to the birefringent material, i.e. optical fibers. Time-Domain Measurement Rabi Oscillation Frequency-Domain Measurement Ramsey Fringe s (s) /(2) (khz)
Quantum Memory for SSL or Two-Color Qubits = 1 A, 0 B + 0 A, 1 B B = 0 A B A A B 1 0 0 2 / 2 = 0.5 / 2 = 1 / 2 = 2 3 s 33 s The shapes of the two retrieved pulses and their energy ratio after the storage time of 3 s are very close to those after the storage time of 33 s.
Quantum Rotator for SSL Qubits = 1 A, 0 B + 0 A, 1 B = 0 B A 0 B A = 0 B B A B1 A B2 A1 A2 1 0 2 1 0 2 B1 A1 A2 1 0 2 B2 (,) = (1,0) s = 15 s (0,1) or (cos,sin) where φ = s One can utilize a two-photon detuning (induced by the Zeeman or AC Stark shift) applied during the storage to change the -to- ratio.
Nonlinear Frequency Conversion Widely-Used Double- Scheme ε A Ω A + Ω B ε B 0.9 1 opt B B,out 2 / A,in 2 OD = 190 A A B A B 0 OD Double-Tripod Scheme ε A Ω A1 + Ω B1 ε B ε A Ω A2 + Ω B2 ε B ε A,out ε B,out ε B,out 2 = e (2φ2 /OD) cos φ sin φ sin φ cos φ 1 0 ε A,in 2 = e (4φ2 /OD) sin 2 φ At = /2, ε B,out 2 ε A,in 2 = e (2 /OD) Better! 0.9 = e (2 /OD) OD = 94
Conclusion We report the first experimental demonstration of twocomponent or spinor slow light (SSL). In a proof-of-principle measurement, our data show that the stored SSL behaves like an interferometer for precise frequency determination. The double tripod scheme can lead to quantum memory for the two-color qubit, i.e. the superposition state of two frequency modes. In the nonlinear frequency conversion, the SSL is a better method than the widely-used double- scheme. 1. M. J. Lee, J. Ruseckas, C. Y. Lee, V. Kudriasov, K. F. Chang, H. W. Cho, G. Juzeliunas, & IAY, Nature Commun. 5, 5542 (2014). 2. 吳京, 唱反調的一對光, 泛科網 http://pansci.tw/archives/73825
http://atomcool.phys.nthu.edu.tw/ Thank you for your attention. Postdoc Position Available in the Rydberg EIT Experiment contact: yu@phys.nthu.edu.tw