e‐ + Interacng Cold Rydberg atoms: A Toy Many‐Body System Antoine Browaeys Instut d’Opque, CNRS Séminaire Poincaré 7 décembre 2013 Many ‐ body systems and complexity Microscopic Quantum laws… Many ‐ body systems and complexity Microscopic Macroscopic ? Quantum laws… quantum or classical laws Many ‐ body systems and complexity Microscopic Macroscopic ? Quantum laws… quantum or classical laws Complexity: for N > 30 – 40, ab‐inio calculaons impossible!! Size of Hilbert space ~2N too large One idea (Feynman 1982): engineer quantum systems in the lab. Measure to find properes you can’t calculate! Applicaons of quantum state engineering Many‐body physics Quantum metrology Quantum informaon Transion quantum / classical Message Exp L Ln Duraon size L Quantum state engineering = control interacons between parcles Atoms and photons Trapped cold ions Cold atoms Quantum state engineering = control interacons between parcles Atoms and photons Trapped cold ions Arficial atoms Cold atoms NV center Supra. circuit Quantum state engineering = control interacons between parcles Atoms and photons Trapped cold ions Arficial atoms Cold atoms NV center Supra. circuit Many‐body toy systems Quantum state engineering = control interacons between parcles Atoms and photons Trapped cold ions Arficial atoms Cold Rydberg atoms NV center Supra. circuit Many‐body toy systems Outline 1. Rydberg atoms and their interacon 2. Rydberg blockade: theorecal aspects 3. Observaon of the Rydberg blockade and collecve excitaon for 2 atoms 4. Rydberg blockade in cold atomic ensembles 5. Applicaon of Rydberg blockade in quantum opcs Outline 1. Rydberg atoms and their interacon 2. Rydberg blockade: theorecal aspects 3. Observaon of the Rydberg blockade and collecve excitaon for 2 atoms 4. Rydberg blockade in cold atomic ensembles 5. Applicaon of Rydberg blockade in quantum opcs Rydberg atoms (alkali case) continuum Rydberg e‐ states + Energy Johannes Rydberg 1854‐1919 Rydberg atoms (alkali case) continuum Rydberg e‐ states + Energy Johannes Rydberg 1854‐1919 Alkali atoms (Rb, Cs) ⇒ hydrogenoid Rydberg atoms (alkali case) continuum Rydberg e‐ states + Energy Johannes Rydberg 1854‐1919 Alkali atoms (Rb, Cs) ⇒ hydrogenoid Screening effect of electronic core: Quantum defect: Properes of Rydberg atoms ~ 100 nm e‐ Bohr model: size + Properes of Rydberg atoms ~ 100 nm e‐ Bohr model: size + 1. Large dipole elements between and for Properes of Rydberg atoms ~ 100 nm e‐ Bohr model: size + 1. Large dipole elements between and for Ex : n ≈ 50 ⇒ 3000 × d(H20) ! Properes of Rydberg atoms ~ 100 nm e‐ Bohr model: size + 1. Large dipole elements between and for Ex : n ≈ 50 ⇒ 3000 × d(H20) ! 2. Large polarizability ⇒ large AC & DC Stark shi Properes of Rydberg atoms ~ 100 nm e‐ Bohr model: size + 1. Large dipole elements between and for Ex : n ≈ 50 ⇒ 3000 × d(H20) ! 2. Large polarizability ⇒ large AC & DC Stark shi 3. Long lifeme ⇒ n > 60, τ > 100 μs Interacon between Rydberg atoms A B + + R Two atom basis: Interacon between Rydberg atoms A B + + R Two atom basis: E ns,ns Interacon between Rydberg atoms A B + + R Two atom basis: E np,(n‐1)p Δ(n) ns,ns Interacon between Rydberg atoms A B + + R Two atom basis: E np,(n‐1)p Δ(n) ns,ns Interacon between Rydberg atoms A B + + R Two atom basis: E np,(n‐1)p Δ(n) ns,ns Interacon between Rydberg atoms A B + + R Two atom basis: E np,(n‐1)p Δ(n) ns,ns Van der Waals: ⇒ Interacon between Rydberg atoms A B + + R Two atom basis: E np,(n‐1)p Δ(n) ns,ns Van der Waals: ⇒ Scaling: Interacon between Rydberg atoms A B + + R Two atom basis: E np,(n‐1)p Δ(n) ns,ns Van der Waals: ⇒ Scaling: Resonant regime: ⇒ Tuning the interacon: Förster resonance E np,(n‐1)p Tune Δ(n): Stark shi Δ(n) ns,ns 87 Ex: for Rb resonance 59d3/2 + 59d3/2 ↔ 57p1/2 + 61f5/2 Tuning the interacon: Förster resonance E np,(n‐1)p Tune Δ(n): Stark shi Δ(n) ns,ns 87 Ex: for Rb resonance 59d3/2 + 59d3/2 ↔ 57p1/2 + 61f5/2 E pf dd gg F (V/cm) Interacon between ”real” Rydberg atoms 87 Ex: Rb atoms in 62d3/2 (L. Béguin) Rydberg interacon: 1011 x ground state + switchable ”Early” experiments and the “need” for cold atoms The “dense Rydberg gas” J‐M Raimond, J. Phys. B 14, L655 (1981) Broadening of excitaon Dense Cs beam ωL ”Early” experiments and the “need” for cold atoms The “dense Rydberg gas” J‐M Raimond, J. Phys. B 14, L655 (1981) Broadening of excitaon Dense Cs beam ωL kBT << Interacon energy ⇒ T < 1 mK ⇒ cold atoms ”Early” experiments and the “need” for cold atoms The “dense Rydberg gas” J‐M Raimond, J. Phys. B 14, L655 (1981) Broadening of excitaon Dense Cs beam ωL kBT << Interacon energy ⇒ T < 1 mK ⇒ cold atoms Many body in “froZen gas” Mourachko, PRL 80, 253 (1998) Diffusion of excitaon faster than moon ⇒ correlaons between all atoms p + p ↔ s + s’ p + s ↔ s + p Outline 1. Rydberg atoms and their interacon 2. Rydberg blockade: theorecal aspects 3. Observaon of the Rydberg blockade and collecve excitaon for 2 atoms 4. Rydberg blockade in cold atomic ensembles 5. Applicaon of Rydberg blockade in quantum opcs Rydberg blockade and collecve excitaon R A B D. Jaksch, et al., PRL 85, 2208 (2000) M. D. Lukin, et al., PRL 87, 037901 (2001) Rydberg blockade and collecve excitaon R A B D. Jaksch, et al., PRL 85, 2208 (2000) M. D. Lukin, et al., PRL 87, 037901 (2001) Rydberg blockade and collecve excitaon R A B If : no excitaon of ⇒ BLOCKADE D. Jaksch, et al., PRL 85, 2208 (2000) M. D. Lukin, et al., PRL 87, 037901 (2001) Rydberg blockade and collecve excitaon R A B Rydberg blockade and collecve excitaon R A B Collecve oscillaon between and with coupling with Blockade sphere and N‐atom collecve excitaon Only one atom excited within a sphere of “blockade” radius Rb Blockade sphere and N‐atom collecve excitaon Only one atom excited within a sphere of “blockade” radius Rb Blockade sphere and N‐atom collecve excitaon Only one atom excited within a sphere of “blockade” radius Rb Coherent excitaon: Ex: 62d3/2, Ω / 2π = 1 MHz ⇒ Rb= 10 μm Blockade sphere and N‐atom collecve excitaon Only one atom excited within a sphere of “blockade” radius Rb Coherent excitaon: Ex: 62d3/2, Ω / 2π = 1 MHz ⇒ Rb= 10 μm N atoms within the blockade sphere ⇒ collecve oscillaon Outline 1. Rydberg atoms and their interacon 2. Rydberg blockade: theorecal aspects 3. Observaon of the Rydberg blockade and collecve excitaon for 2 atoms 4. Rydberg blockade in cold atomic ensembles 5. Applicaon of Rydberg blockade in quantum opcs Microscopic opcal dipole trap |e〉 Non‐resonant atom‐laser interacon ⇒ light‐shi I |g〉 ~ I Microscopic opcal dipole trap |e〉 Non‐resonant atom‐laser interacon ⇒ light‐shi I |g〉 ~ I Dipole trap light High NA lens Size ~ 1 µm Dichroic Volume ~ 1 µm3 mirror Depth ≈ 1 mK ⇒ laser cooled atoms Microscopic opcal dipole trap |e〉 Non‐resonant atom‐laser interacon ⇒ light‐shi I |g〉 ~ I Resonant laser Dipole trap light High NA lens Fluorescence Dichroic photon counter, mirror camera Laser ‐ cooled atoms Schlosser et al., Nature 411, 1024 (2001) T ~ 100 µK Sortais et al., PRA 75, 013406 (2007) Loading the trap with individual atoms Loading rate Cooling lasers w v Light‐assisted loss in the trap Loss ~ 1/ trap size Prevents 2 trapped atoms when loss >> loading Trapping a single (cold) atom Fluorescence @ 780 nm induced by the cooling lasers 100 80 60 40 20 ount / 10 ms 0 C 8.5 9.0 9.5 10.0 10.5 11.0 11.5 Time (s) Schlosser et al., Nature 411, 1024 (2001); Sortais et al., PRA 75, 013406 (2007) Trapping a single (cold) atom Fluorescence @ 780 nm induced by the cooling lasers 100 80 1 atom 60 40 0 atom 20 ount / 10 ms 0 C 8.5 9.0 9.5 10.0 10.5 11.0 11.5 Time (s) NON determinisc single‐atom source Schlosser et al., Nature 411, 1024 (2001); Sortais et al., PRA 75, 013406 (2007) Coherent excitaon of atoms to Rydberg state (ex: 87Rb) 2‐photon excitaon: 475 nm 795 nm Coherent excitaon of atoms to Rydberg state (ex: 87Rb) 2‐photon excitaon: 475 nm Prepare: 795 nm Coherent excitaon of atoms to Rydberg state (ex: 87Rb) 2‐photon excitaon: 475 nm Prepare: 795 nm Result of a single measurement: OR ⇒ must repeat to calculate Pr (x 100) Coherent excitaon of atoms to Rydberg state (ex: 87Rb) 2‐photon excitaon: 475 nm Prepare: 795 nm Result of a single Ω/2π = 0.9 MHz measurement: OR r P ⇒ must repeat to calculate Pr (x 100) 58d3/2 Demonstraon of the Rydberg blockade: U. Wisconsin Addressable excitaon A 10 μm B E. Urban et al., Nat. Phys. 5, 110 (2009) Demonstraon of the Rydberg blockade: U. Wisconsin Addressable excitaon Oscillaon of atom B g A 10 μm B P 90d5/2 E. Urban et al., Nat. Phys. 5, 110 (2009) Demonstraon of the Rydberg blockade: U. Wisconsin Addressable excitaon Oscillaon of atom B g A 10 μm B P 90d5/2 Excitaon of atom B condionned by the state of atom A ⇒ Demonstraon of C‐NOT gate and entanglement Isenhower et al., PRL 104, 010503 (2010) Rydberg blockade and collecve excitaon: Instut d’Opque Exc. proba atom A only A 795 nm 474 nm 58d3/2 Gaëtan et al., Nat. Phys. 5, 115 (2009) Rydberg blockade and collecve excitaon: Instut d’Opque Exc. proba atom A only A Exc. proba atom A & B R = 5 μm 795 nm B BLOCKADE 474 nm 58d3/2 Gaëtan et al., Nat.