Quantum optics and quantum information processing with superconducting circuits

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

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

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)

Q 3 Energy [a.u.] V (t) = V cos 1 t Artificial atoms: a toolkit 2 1 1 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

Artificial atoms: potential shaping Energy [a.u.] 1 t Q Standard toolkit I= Capacitor Inductor Resistor Wire 2 1 1 /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 / )

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

Artificial atoms: fast and coherent V (t) = V cos 1t Energy [a.u.] 1 2 3 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.], 1999 2 22 26 27 211 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:115.4652v2 (211)?

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)

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

From cavity to circuit QED E-field can be tightly confined E/ p 1/ 3 3 1 1 4 Large zero-point fluctuations of the field: E.2 V/m Blais, Huang, Wallraff, Girvin & Schoelkopf, Phys. Rev. A 69, 6232 (24)

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)

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)

On-demand single microwave-photon source + 1.4 b 1.2 First experimental steps towards single microwave-photon detectors 5 µm <σz> <a a> On-demand single microwave photon source 1 2 4 6 8 1 Rabi angle (rad) A. Houck et al. Nature 449, 328 (27) Y.-F. Chen et al. arxiv:111.4329 D. Bozyigit,..., M. P. da Silva, A. Blais and A. Wallraff. Nature Physics 7, 154 (211)

On-demand single microwave-photon source + 1.4 b 1.2 First experimental steps towards single microwave-photon detectors 5 µm <σz> <a a> On-demand single microwave photon source g 1 2 4 6 8 1 Rabi angle (rad) A. Houck et al. Nature 449, 328 (27) Y.-F. Chen et al. arxiv:111.4329 D. Bozyigit,..., M. P. da Silva, A. Blais and A. Wallraff. Nature Physics 7, 154 (211)

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)

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)

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)

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

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

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/

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)

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)

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.1.2.3 t Ms.4.5 t/2 e / sin( r )e.5.4.3.2.1.. Amplitude arb. 1 a b f t/2 /2 ge Se(t) gf Sf(t) i.4.2..2.4 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)

Same-time averages a t a t Rabi angle Qr 2P 3P 4.51 2 3.45 P 1 S e (t)s f (t) 1 P i = ( i + 1i) 1 2 Power arb. 4.4 4.2 4. 3.8 3.6 Power arb. = 2 e t.1.2.3 t Ms.4 + P (Nef ) Can be (mostly) subtracted away with measurements in the ground state e. 4.4 4.2 4. 3.8 3.6 3.4 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)

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, 13361 (21)

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)

Two-time correlation functions: G (2) ( ) 1. G 2 Τ norm..5. 1..5. 1. 1 Αr.9 G (2) () = G (2) (nt p ) / sin 4 ( r /2) 1..8.6.4.2..5 Π 2 Π. Rabi angle Θ r 2 1 1 2 3 4 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)

Two-time correlation functions: G(2)( )!" 1..5 G(2) () = G#2$ #Τ$ %norm.&.!1" 1. G(2) (ntp ) / sin4 ( r /2) 1..8.6.4.2..5.!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)

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