Quantum optics and quantum information processing with superconducting circuits

Transcription

1 Quantum optics and quantum information processing with superconducting circuits Alexandre Blais Université de Sherbrooke, Canada Sherbrooke s circuit QED theory group Félix Beaudoin, Adam B. Bolduc, Maxime Boissonneault, Jérôme Bourassa, Samuel Boutin, Andy Ferris, Kevin Lalumière, Clemens Mueller, Matt Woolley Former members: Marcus da Silva, Gabrielle Denhez

2 Microwave-photon antibunching without clicks Alexandre Blais Université de Sherbrooke, Canada Sherbrooke s circuit QED theory group Félix Beaudoin, Adam B. Bolduc, Maxime Boissonneault, Jérôme Bourassa, Samuel Boutin, Andy Ferris, Kevin Lalumière, Clemens Mueller, Matt Woolley Former members: Marcus da Silva, Gabrielle Denhez Quantum Device Lab, ETH Zurich Deniz Bozyigit, C. Lang, L. Steffen, J. M. Fink, M. Baur, R. Bianchetti, P. J. Leek, S. Filipp, Andreas Wallraff

3 Energy [a.u.] Nature s atoms 1 Good «two-level atom» approximation 2 E1 = E1 E = ~ 1 Position [a.u.] Control internal state by shining laser tuned at the transition frequency H= d E(t) with Hyperfine levels of 9Be+ have long decay and coherence times T1 a few years T2 & 1 seconds E(t) = E cos 1 t Reasonably short π-pulse time T 5 µs Low error per gates: ~.48% T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, and J. L. O Brien, Nature 464, 45 (21)

4 Q 3 Energy [a.u.] V (t) = V cos 1 t Artificial atoms: a toolkit p = 1/ LC Standard toolkit Flux [a.u.] Capacitor Simple initialization to ground state Inductor 1 Resistor Wire p = 1/ LC 1 GHz.5 K Not a good «two-level» atom... 3 K 1 mk

5 Artificial atoms: potential shaping Energy [a.u.] 1 t Q Standard toolkit I= Capacitor Inductor Resistor Wire /L p = 1/ LC Flux [a.u.] Josephson junctions V (t) = V cos 3 I = I sin(2 / I LJ ( ) = = ) 1 2 I cos(2 1 / )

6 V (t) = V cos 1 t Energy [a.u.] Artificial atoms: potential shaping Capacitor Inductor Resistor Wire Josephson junctions Standard toolkit Flux [a.u.] I = I sin(2 / I LJ ( ) = = ) 1 2 I cos(2 1 / )

7 Artificial atoms: fast and coherent V (t) = V cos 1t Energy [a.u.] Very short π-pulse time T 4 2 ns Big improvements in relaxation and dephasing times Error per gates of.25%, similar to trapped ion results T2 [µs] 1, 1, 1,,1,1 Flux [a.u.], Year 1, 1, 1,,1, T1 [µs] Short pulse: J. M Chow et al, Phys. Rev. A 82, 435(R) (21) Long coherence: H. Paik et al, arxiv: v2 (211)?

8 Energy [a.u.] From atomic physics to quantum optics 1 Good «two-level atom» approximation 2 E1 = E1 E = ~ 1 Position [a.u.] Control internal state by shining laser at the transition frequency d E(t) { H= with g Can the field of a single photon, or even vacuum fluctuations, have a large effect? E(t) = E cos 1 t Cavity QED 1) Work with large atoms (d) 2) Confine the field (E) Exploring the Quantum: Atoms, Cavities, and Photons, S. Haroche and J.-M. Raimond (26)

9 From cavity to circuit QED Artificial atoms are large ~ 3 µm V(t)

10 From cavity to circuit QED E-field can be tightly confined E/ p 1/ Large zero-point fluctuations of the field: E.2 V/m Blais, Huang, Wallraff, Girvin & Schoelkopf, Phys. Rev. A 69, 6232 (24)

11 From cavity to circuit QED Atom : Transmon qubit of transition frequency ω a and long coherence time Cavity : Superconducting coplanar transmission-line resonator of fundamental mode frequency ω r g circuit /2 [ 1] GHz g cavity /2 5 khz Proposal: Blais, Huang, Wallraff, Girvin & Schoelkopf, Phys. Rev. A 69, 6232 (24) First realization: Wallraff, Schuster, Blais, Frunzio, Huang, Majer, Kumar, Girvin & Schoelkopf. Nature 431, 162 (24) Ultra-strong coupling: Bourassa, Gambetta, Abdumalikov, Astafiev, Nakamura & Blais. Phys. Rev. A 8, 3219 (29)

12 Quantum optics with circuit QED Signature of quantum nature of light How to characterize this single microwave-photon source? 1 2 x Δt 1 2Δt 1 3Δt 1 : : : : Counts t n1 n2 x Delay G(2) ( ) = ha (t + )a (t)a(t + )a(t)i D. F. Walls and G. J. Milburn. Quantum Optics (28)

13 On-demand single microwave-photon source b 1.2 First experimental steps towards single microwave-photon detectors 5 µm <σz> <a a> On-demand single microwave photon source Rabi angle (rad) A. Houck et al. Nature 449, 328 (27) Y.-F. Chen et al. arxiv: D. Bozyigit,..., M. P. da Silva, A. Blais and A. Wallraff. Nature Physics 7, 154 (211)

14 On-demand single microwave-photon source b 1.2 First experimental steps towards single microwave-photon detectors 5 µm <σz> <a a> On-demand single microwave photon source g Rabi angle (rad) A. Houck et al. Nature 449, 328 (27) Y.-F. Chen et al. arxiv: D. Bozyigit,..., M. P. da Silva, A. Blais and A. Wallraff. Nature Physics 7, 154 (211)

15 Quantum mechanics of microwave measurements â ˆb g b ˆbamp apple b Output field: ˆb(t) = p bâ(t) ˆbin (t)? Amplification: b amp (t) =g b b(t) ) [b amp (t),b amp(t)] = g 2 b C. W. Gardiner and M. J. Collett, Phys. Rev. A 31, 3761 (1985); C. M. Caves, Phys. Rev. D 26, 1817 (1982) B. Yurke and J. S. Denker, Phys. Rev. A 29, 1419 (1984); A. Clerk et al., Rev. Mod. Phys. 82, 1155 (21)

16 Quantum mechanics of microwave measurements I â apple b ˆb g b Q Output field: Amplification: ˆb(t) = p bâ(t) b amp (t) =g b b(t)+ with ˆbin (t) q g 2 b 1d b (t) hd b (t)d b(t )i = N T (t t ) Added noise C. W. Gardiner and M. J. Collett, Phys. Rev. A 31, 3761 (1985); C. M. Caves, Phys. Rev. D 26, 1817 (1982) B. Yurke and J. S. Denker, Phys. Rev. A 29, 1419 (1984); A. Clerk et al., Rev. Mod. Phys. 82, 1155 (21)

17 Quantum mechanics of microwave measurements Ib Xb / (b + b) Pb / i(b ^ b a Xb gb b Output field: b (t) = p b a (t) with ^ Pb i Qb b in (t) Amplification: bamp (t) = gb b(t) + hdb (t)db (t )i b) q gb2 = NT (t 1d b (t) Added noise t ) Beam-splitter: added vacuum noise and commuting outputs C. W. Gardiner and M. J. Collett, Phys. Rev. A 31, 3761 (1985); C. M. Caves, Phys. Rev. D 26, 1817 (1982) B. Yurke and J. S. Denker, Phys. Rev. A 29, 1419 (1984); A. Clerk et al., Rev. Mod. Phys. 82, 1155 (21)

18 Complex envelope â apple b ˆb g b I b ^ X b i ^ P b Q b X b / (b + b) P b / i(b b) Complex envelope: Ŝ b (t) = ˆX b (t)+i ˆP b (t) = g bˆb(t)+ ˆNb (t) = g b p bâ(t)+ ˆN b(t) Digitalized using FPGA electronics with a 1 ns time resolution 1/apple

19 Beam-splitter: Noise rejection X b / (b + b) P b / i(b b) â apple b ˆb g b S b (t) Complex envelope: Ŝ b (t) = ˆX b (t)+i ˆP b (t) = g bˆb(t)+ ˆNb (t) = g b p bâ(t)+ ˆN b(t) Digitalized using FPGA electronics with a 1 ns time resolution 1/apple

20 Beam-splitter: Noise rejection ge e b a b fˆ gf i Complex envelope: S b (t) = X b (t) + ip b (t) Se(t) Sf(t) Rejection of uncorrelated noise = gb b (t) + N b (t) p = gb b a (t) + N b (t) Digitalized using FPGA electronics with a 1 ns time resolution 1/

21 Same-time averages ge e b a b fˆ gf i Se(t) Sf(t) Same-time averages: Quadrature hs e (t)i ha (t)i Cross-power hs e (t)s f (t)i ha (t)a (t)i M. P. da Silva, D. Bozyigit, A. Wallraff, A. Blais. Phys. Rev. A 82, 4384 (21) D. Bozyigit,..., M. P. da Silva, A. Blais and A. Wallraff. Nature Physics 7, 154 (211)

22 Protocol e Repeat ~ 16-9 times 1. Cool to ground state 1i = gi i a 2i 3i Se(t) gf Sf(t) = ( gi + ei) i 3. Transfer state to resonator f i 2. Prepare arbitrary qubit state b ge = gi ( i + 1i) r = cos( r /2) = sin( r /2)ei 4. Measure quadratures, extract Se,f(t) and calculate desired quantity 5. Average results M. P. da Silva, D. Bozyigit, A. Wallraff, A. Blais. Phys. Rev. A 82, 4384 (21) D. Bozyigit,..., M. P. da Silva, A. Blais and A. Wallraff. Nature Physics 7, 154 (211)

23 Same-time averages Re a t 2P.5.5 Rabi angle Qr 3P 2 P 1 P Amplitude arb. 2 1 i = ( i + 1i) hs e (t)i / ha (t)i = e t Ms.4.5 t/2 e / sin( r )e Amplitude arb. 1 a b f t/2 /2 ge Se(t) gf Sf(t) i P2 P Rabi angle 3P 2 Qr 2P See also: A. A. Houck et al. Nature 449, 328 (27) M. P. da Silva, D. Bozyigit, A. Wallraff, A. Blais. Phys. Rev. A 82, 4384 (21) D. Bozyigit,..., M. P. da Silva, A. Blais and A. Wallraff. Nature Physics 7, 154 (211)

24 Same-time averages a t a t Rabi angle Qr 2P 3P P 1 S e (t)s f (t) 1 P i = ( i + 1i) 1 2 Power arb Power arb. = 2 e t t Ms.4 + P (Nef ) Can be (mostly) subtracted away with measurements in the ground state e a (t)a (t) + P (Nef ).5 a b f ge Se(t) gf Sf(t) i P2 P Rabi angle 3P 2 Qr 2P See also: A. A. Houck et al. Nature 449, 328 (27) M. P. da Silva, D. Bozyigit, A. Wallraff, A. Blais. Phys. Rev. A 82, 4384 (21) D. Bozyigit,..., M. P. da Silva, A. Blais and A. Wallraff. Nature Physics 7, 154 (211)

25 Two-time averages ge e fˆ b a b i gf Se(t) Sf(t) Two-time correlation functions: hs e (t)s f (t + )i = p ge gf (1) G (t, t + ) + N ef ( ) 2 G(1) ( ) = ha (t)a(t + )i ge gf (2) (2) + )S f (t + )S f (t)i = G (t, t + ) + Gnoise (t, t + ) 4 p h i ge gf + N ef ( )G(1) (t +, t) ()G(1) (t +, t + ) + ()G(1) (t, t) + ( )G(1) (t, t + ) 2 hs e (t)s e (t M. P. da Silva, D. Bozyigit, A. Wallraff, A. Blais. Phys. Rev. A 82, 4384 (21) D. Bozyigit,..., M. P. da Silva, A. Blais and A. Wallraff. Nature Physics 7, 154 (211) See also: Menzel et al., Phys. Rev. Lett. 15, 141 (21); Mariantoni et al., Phys. Rev. Lett. 15, (21)

26 Two-time correlation functions: G (2) ( ) Second order cross-correlation: hŝ e(t)ŝ e(t + )Ŝf (t + )Ŝf (t)i = g eg f 4 G(2) (t, t + )+G (2) noise (t, t + ) p ge g f h i + N ef ( )G (1) (t +,t) ()G (1) (t +,t+ )+ ()G (1) (t, t)+ ( )G (1) (t, t + ) 2 G (2) ( )=ha (t + )a (t)a(t + )a(t)i Pulsed single-microwave photon source - Pulse delay: t p = 512 ns 1/, 1/T 1 - Expected results: G 2 ( = nt p ) / sin 4 ( r /2) G 2 () = M. P. da Silva, D. Bozyigit, A. Wallraff, A. Blais. Phys. Rev. A 82, 4384 (21) D. Bozyigit,..., M. P. da Silva, A. Blais and A. Wallraff. Nature Physics 7, 154 (211)

27 Two-time correlation functions: G (2) ( ) 1. G 2 Τ norm Αr.9 G (2) () = G (2) (nt p ) / sin 4 ( r /2) Π 2 Π. Rabi angle Θ r Τ Μs M. P. da Silva, D. Bozyigit, A. Wallraff, A. Blais. Phys. Rev. A 82, 4384 (21) D. Bozyigit,..., M. P. da Silva, A. Blais and A. Wallraff. Nature Physics 7, 154 (211)

28 Two-time correlation functions: G(2)( )!" 1..5 G(2) () = G#2$ #Τ$ %norm.&.!1" 1. G(2) (ntp ) / sin4 ( r /2) !Αr ".9" 1. Wigner function reconstruction of itinerant.5 microwave photon Π!2 Rabi angle.!2!1 1 Τ!Μs" 2 3 Π Θr 4 C. Eichler et al, Phys. Rev. Lett. 16, 2253 (211) M. P. da Silva, D. Bozyigit, A. Wallraff, A. Blais. Phys. Rev. A 82, 4384 (21) D. Bozyigit,..., M. P. da Silva, A. Blais and A. Wallraff. Nature Physics 7, 154 (211)

29 Summary Quantum information processing Antibunching: Quantum nature of microwave light demonstrated Correlations characterize output field Quantum mechanics on large length scales On-demand single photon source Superconducting high-q resonator Transmon qubits with long coherence times