Cooperative atom-light interaction in a blockaded Rydberg ensemble

Transcription

1 Cooperative atom-light interaction in a blockaded Rydberg ensemble α 1 Jonathan Pritchard University of Durham, UK

2 Overview 1. Cooperative optical non-linearity due to dipole-dipole interactions 2. Observation of cooperativity in an ultra-cold Rydberg ensemble 3. Towards single photon non-linearities

3 Photonic Quantum Computer Photon Source Single Photon Gate λ 2 Photon Detector Two Photon Gate No free-space photonphoton interaction KLM Linear Optics E. Knill et al. Nature 409, 46 (2001) Nonlinear atom-light interaction Rydberg atoms I. Freidler et al. PRA 72, (2005)

4 Optical Non-linearity Optical response expressed in terms of complex susceptibility: χ = χ (1) + χ (2) E + χ (3) E 2 + l k =2π/λ Observe back-action on light : Transmission T = exp{ kχ I l} Dispersion φ = kχ R l/2

5 Electromagnetically Induced Transparency Consider a three level atom in ladder EIT scheme r On resonance eigenstate is: p Γ r e Ψ = (Ω2 p + Γ 2 e) 1/2 g Ω p e 2(Ω 2 p/2+γ 2 e/4) 1/2 Ψ = Ω p Γ e g Susceptibility:! "#$ "#' χi/χ0 "#& "#% Γ e χr/χ0 " "#$ "!! "!!"#$!! "! p /Γ e p /Γ e

6 Electromagnetically Induced Transparency Consider a three level atom in ladder EIT scheme Ω c > Ω p c p Ω c r Γ r e On two-photon resonance populate dark state: Ψ D = Ω c g Ω p r (Ω 2 p + Ω 2 c) 1/2 Ψ D = Ω p Γ e g χi/χ0 Susceptibility:! "#' "#& "#% "#$ "!! "! p /Γ e M. Fleischhauer et al., RMP 77, 633 (2005). χr/χ0 "#$ "!"#$!! "! p /Γ e Intensity dependent Giant Kerr χ (3) H. Schmidt and A. Imamo!lu Opt. Lett. 21, 1936 (1996) A. Mohapatra et al. Nature Phys. 4, 890 (2008)

7 Single photon Kerr non-linearities Apply Kerr effect to two photon gate: χ (3) Phase shift changes across envelope - destroys fidelity Single-photon Kerr non-linearities do not help quantum computation, J. H. Shapiro, PRA 76, (2006) Impossibility of large phase shift via the giant Kerr effect with single photon wavepackets, J. Gea-Banacloche, PRA 81, (2010). Require novel non-linearity

8 Cooperative Non-linearity Ordinary Non-linearity Single dipole χ 1 Two dipoles + Dipoles Independent χ =2χ 1 From single dipole response derive response of ensemble χ = Nχ 1 Cooperative non-linearity Introduce strong dipole-dipole interactions Two dipoles + Dipoles Correlated χ 2χ 1 Optical response of single dipole modified by neighbouring dipoles

9 Rydberg Atoms Cooperativity requires strong dipole-dipole interactions Rydberg Atoms Dipole moment µ n 2 Interaction V (R) = C 6 R 6 n11 Strong dipole-dipole interactions Blockade V (R) > Ω c W rr Blockade radius gr R b = 6 C6 Ω c 5 µm (60S 1/2, Ω c 4 MHz) gg Average Number of atoms / blockade R N b =4/3πR 3 bρ

10 Rydberg EIT without interactions Consider a pair of atoms R R b rr r 1 r 2 er re Ω c e 1 Ω c e 2 gr ee rg Ω p Ω p ge eg g 1 g 2 Atom 1 Atom 2 gg Coupled Basis Large separation : Observe ordinary dark state Ψ D = ψ D 1 ψ D 2 Ψ D =, + = χ 1 + χ 2 = χ

11 Rydberg EIT with interactions Move atoms closer R < R b V (R) rr r 1 V (R) r 2 er re Ω c e 1 Ω c e 2 gr ee rg Ω p Ω p ge eg Atom 1 g 1 Atom 2 g 2 gg Coupled Basis V (R) Ω c : Blockade creates new state Ψ D. Møller et al. PRL 100, (2008), Ψ = +, Tuneable cooperative atom-light interaction + = χ 1 + χ 2 = χ Ω c, Ω p,v(r)

12 Overview 1. Cooperative optical non-linearity due to dipole-dipole interactions 2. Observation of cooperativity in an ultra-cold Rydberg ensemble 3. Towards single photon non-linearities

13 Experiment Setup EIT Locking Scheme ns np Choice of Rydberg State V (R) > Ω c > Ω p C 6 n 11 Ω c n 3/2 n = Coupling Laser 480 nm Experimental Setup 87 Rb atoms prepared in 5S1/2 F =2,m F =2 Probe Laser 780 nm 5s 5p R. P. Abel et al., Appl. Phys. Lett. 94, (2009) P pw 3 nw w 0 = 12 µm σ 2G Bias P mw w 0 = 66 µm σ + Single Photon Counter Scan probe p /2π = MHz in 500 µs K. J. Weatherill et al., J. Phys. B 41, (2008).

14 5S1/2! 5P3/2! 60S1/2 Transmi ssi on Record transmission for 60S1/2 at ρ cm 3 Ω c /2π =0 4.8 MHz "$* Ω p /2π Data recorded from 100 averages "$) (MHz ) 0.3 Weak probe : "$( "$# "$' "$& "$% "$! "!!"!# " #!" p /2π (MHz) J. D. Pritchard et al. arxiv: (2010)

15 5S1/2! 5P3/2! 60S1/2 Transmi ssi on Record transmission for 60S1/2 at Ω c /2π 4.8 MHz "$* "$) "$( "$# "$' "$& "$% "$! Ω p /2π (MHz ) 0.3 Weak probe : "!!"!# " #!" p /2π (MHz) J. D. Pritchard et al. arxiv: (2010) ρ cm 3 Data recorded from 100 averages No Rydberg population Narrow probe of Rydberg state frequency

16 5S1/2! 5P3/2! 60S1/2 Transmi ssi on Record transmission for 60S1/2 at Ω c /2π 4.8 MHz "$* "$) "$( "$# "$' "$& "$% Ω p /2π (MHz ) > 50 % ρ cm 3 + Suppression "$! "!!"!# " #!" p /2π (MHz) J. D. Pritchard et al. arxiv: (2010)

17 5S1/2! 5P3/2! 60S1/2 Transmi ssi on Record transmission for 60S1/2 at Ω c /2π 4.8 MHz "$* "$) "$( "$# "$' "$& "$% Ω p /2π (MHz ) γ ρ cm 3 + Suppression + No broadening "$! "!!"!# " #!" p /2π (MHz) J. D. Pritchard et al. arxiv: (2010)

18 5S1/2! 5P3/2! 60S1/2 Transmi ssi on Record transmission for 60S1/2 at Ω c /2π 4.8 MHz "$* δ "$) "$( "$# "$' "$& "$% Ω p /2π (MHz ) ρ cm 3 + Suppression + No broadening + No shift "$! "!!"!# " #!" p /2π (MHz) J. D. Pritchard et al. arxiv: (2010)

19 Mechanisms for suppression Observations: Suppression No Shift No Broadening Mechanisms: Ion Creation Mean-field interaction Van der Waals dephasing Cooperative Nonlinearity

20 Mechanisms for suppression Observations: Suppression No Shift No Broadening Mechanisms: Ion Creation Mean-field interaction Van der Waals dephasing ion Ω c Ω p r e Stark shift of atom i i ion = 1 2 α 0 N ion j E 2 (R ij ) Cooperative Nonlinearity g "$+ "$* Ion Density 0 % 5 % 10 % 20 % Ions cause red shift and broadening Transmi ssi on "$) "$( "$# "$' "$& "$% "$! "!!"!# " #!" p /2π (MHz)

21 Mechanisms for suppression Observations: Suppression No Shift No Broadening Mechanisms: Ion Creation Mean-field interaction Van der Waals dephasing dd r Dipole-dipole shift of atom i Ω c N i dd = C 6 e Rij 6 Ω p i j Cooperative Nonlinearity g "$+ "$* Rydberg Density 0 % 0.25 % 0.5 % 1% Mean-field causes blue shift and broadening H. Schempp et al. PRL 104, (2010) Transmi ssi on "$) "$( "$# "$' "$& "$% "$! "!!"!# " #!" p /2π (MHz)

22 Mechanisms for suppression Observations: Suppression No Shift No Broadening Mechanisms: Ion Creation Mean-field interaction Van der Waals dephasing Cooperative Nonlinearity γ Ω c Ω p r e g Dephasing Rate γ = γ vdw N r Fit 60S data: γ vdw 7Γ e γ /Γ e!"#( "#& "#% "#$ " ( $ ) %! Ω p /2π (MHz) vdw predicts significant broadening M. Gross and S. Haroche Phys. Rep. 93, 301 (1982) Transmi ssi on Ω p /2π: 0.1 MHz "!! "! "#' "#& "#% "#$ "#( 2 MHz!! "!!! "! p /2π (MHz) 4 MHz

23 Mechanisms for suppression Observations: Suppression No Shift No Broadening Mechanisms: Ion Creation Mean-field interaction Van der Waals dephasing Cooperative Nonlinearity Require model for all atoms in blockade ρ cm 3 N b 9 Transmi ssi on "$* "$) "$( "$# "$' "$& "$% "$! Ω p /2π (MHz ) Too big to model! "!!"!# " #!" p /2π (MHz)

24 5S1/2! 5P3/2! 60S1/2 Reduce atomic density ρ cm 3 N b 3 Require 3-atom model Ω p /2π (MHz) : ) Transmi ssi on "#( "#' "#& "#% "#! "#$!! "!!! "!!! "! p /2π (MHz)

25 Three Atom Model (1) Three Atom Coupled Basis Ω p Ω c Blockaded States Entangled state on two-photon resonance: Ψ = +,,,,,, + Model transmission using Liouville eq. σ = i [σ, H ] γσ

26 Parameters: weak-probe data Ω c /2π =3.8 MHz γ gr /2π = 110 khz Interaction strength: 1 Three Atom Model (2) V/2π = 15 MHz Ω p /2π (MHz) : Transmi ssi on ) "#( "#' "#& "#% "#! "#$!! "!!! "!!! "! p /2π (MHz) Transmi ssi on Data 1 Atom 2 Atoms 3 Atoms Ω p /2π (MHz) Cooperative Nonlinearity :! Suppression! No Shift! No Broadening J. D. Pritchard et al. arxiv: (2010)

27 Blockade Dephasing Rate Cooperative model: Transmi ssi on ) "#( "#' "#& "#% "#! "#$!! "!!! "!!! "! p /2π (MHz) Model single blockade to reproduce ensemble No additional broadening EIT width limited by relative laser linewidth γ gr Blockade dephasing rate γ b /2π < 100 khz

28 Nb-Scaling Non-linear density scaling: 1 N b (N b 1) + N = b Ω p /2π (MHz) S 1/2 Number of atoms / blockade: 0.4 N b ρr 3 b n 6.25 χ EIT I χ ABS I S 1/2 N b 60 Nb 54 = Measured ratio 2.6 ± ρ ( cm 3 ) J. D. Pritchard et al. arxiv: (2010) N b

29 Overview 1. Cooperative optical non-linearity due to dipole-dipole interactions 2. Observation of cooperativity in an ultra-cold Rydberg ensemble 3. Towards single photon non-linearities

30 Photon Blockade α Input light in coherent state α P (n) n =2 Ensemble transparent to single photon,, Ψ = + n,, +,, Measure changes in photon statistics due to cooperative interaction

31 Blockaded Ensemble " Single Photon source M. Saffman and T. Walker, PRA 66, (2002) " Cooperative emission of a single photon D. Porras and J. I. Cirac, PRL 78, (2009) L. H. Pedersen and K. Mølmer, PRA 79, (2009)

32 Single Photon Non-linearities Requirements: + Large single photon Rabi frequency + All atoms confined within single blockade sphere R < R b 5 µm Solution: Microscopic Dipole Trap 915 nm dipole trap 780 nm probe beam Transverse trap w =6µm

33 Vacuum Chamber

34 Outlook Cooperative atom-light interaction due to dipole-dipole interactions! Done Transmission "$* "$) "$( "$# "$' "$& "$% "$! Ω p /2π (MHz ) "!!"!# " #!" p /2π (MHz) Require single blockade sphere! Built Explore photon statistics! In progress

35 Acknowledgements Dan Maxwell Dr. Alex Gauguet Dr. Kevin Weatherill Dr. Matt Jones Prof. Charles Adams