Quantum simulation of the Rabi model in a trapped ion system

Transcription

1 Quantum simulation of the Rabi model in a trapped ion system Dingshun Lv 1, Shuoming An 1,Zhenyu Liu 1, Jing-Ning Zhang 1 Julen S. Pedernales 2, Lucas Lamata 2, Enrique Solano 2,3, Kihwan Kim 1 1 CQI, IIIS, Tsinghua University 2 Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, Bilbao, Spain 3 IKERBASQUE, Basque Foundation for Science, Alameda Urquijo 36, Bilbao, Spain lds12@mails.tsinghua.edu.cn September 7, 2017 (CQI, IIIS, Tsinghua University, Beijing) Kihwan Kim s group September 7, / 15

2 Outline 1 Background of the Rabi model 2 Experimental setup and proposal to simulate QRM with trapped ion system 3 Experimental results (CQI, IIIS, Tsinghua University, Beijing) Kihwan Kim s group September 7, / 15

3 Background of the Rabi model:why quantum Rabi model? Originally, Rabi model was proposed in 1936 to deal with the effect of a varying, weak magnetic field on an oriented atom possessing nuclear. Rabi I I. On the process of space quantization[j]. Physical Review, 1936, 49(4): 324. With full quantized field, we get the quantum version of Rabi model, describe as H QRM = 1 2 ħω σ z + ħω m a a + ħg σ + + σ a + a it can extend to Jaynes-Cummings model via the rotate wave approximation(rwa)(g ω m ) H JCM = 1 2 ħω σ z + ħω m a a + ħg a σ + + a σ Recently an analytic solution has been proposaled that cover all the coupling regime and experiments has push into the USC/DSC regime, where RWA, JCM is not applicable, and full QRM is required. (USC: 1 g/ω m, DSC: 1 g/ω m ) Braak D. Integrability of the Rabi model[j]. Physical Review Letters, 2011, 107(10): (CQI, IIIS, Tsinghua University, Beijing) Kihwan Kim s group September 7, / 15

4 Recent achievements in USC/DSC regime Crespi et al. "Photonic realization of the quantum Rabi model." Physical review letters (2012): Langford, N. K., et al. "Experimentally simulating the dynamics of quantum light and matter at ultrastrong coupling." arxiv preprint arxiv: (2016). Forn-Díaz, P., et al. "Ultrastrong coupling of a single artificial atom to an electromagnetic continuum in the nonperturbative regime." Nature Physics 13.1 (2017): Yoshihara, Fumiki, et al. "Superconducting qubit-oscillator circuit beyond the ultrastrong-coupling regime." Nature Physics (2016). (CQI, IIIS, Tsinghua University, Beijing) Kihwan Kim s group September 7, / 15

5 Experimental setup and proposal to simulate QRM with trapped ion system 171 Yb + 2 P 1/2 Bichromatic lasers Raman1 δb, n +1, n F=1 δr, n -1 State initialization to:, 0 State detection: florensence collection : no photons collected : photons collected 2 S 1/2 ωhf F=0, n +1, n, n -1 Pedernales J S, Lizuain I, Felicetti S, et al. Quantum Rabi model with trapped ions[j]. Scientific reports, 2015, 5. (CQI, IIIS, Tsinghua University, Beijing) Kihwan Kim s group September 7, / 15

6 Ion-light interaction The total Hamiltonian of the ion-light matter interaction include three parts, written as Ĥ = Ĥ m + Ĥ e + Ĥ i (1) Here Ĥ m of the motional model X can be written as Ĥ m = ω X (â â ) (2) Ĥ e describes the internal electronic level structure of spin down and spin up, written as Ĥ e = ω HF 2 σ Z (3) the ion-light interaction part Ĥ i = Ω 2 (σ + + σ )(e i( k x ωt+φ) + e i( k x ωt+φ) ), (4) (CQI, IIIS, Tsinghua University, Beijing) Kihwan Kim s group September 7, / 15

7 Ion-light interaction In the interaction picture Ĥ0 = Ĥm + Ĥe, = ω ω HF If = 0, we get the carrier transition Hamiltonian, Ĥ car (φ) = Ω 2 (ˆσ +e iφ + ˆσ e iφ ). (5) If = ω X, we get the red sideband transition Hamiltonian or the Jaynes-Cummings(JC) coupling, Ĥ JC (φ) = i ηω 2 (ˆσ â e iφ ˆσ + âe iφ ), (6) If = ω X, we get the blue sideband transition Hamiltonian or the anti-jaynes-cummings(ajc)coupling Ĥ ajc (φ) = i ηω 2 (ˆσ +â e iφ ˆσ âe iφ ). (7) (CQI, IIIS, Tsinghua University, Beijing) Kihwan Kim s group September 7, / 15

8 Simulate Quantum Rabi model Remind that the Quantum Rabi Model(QRM) is written as Ĥ R = 1 2 ωˆσ z + ω m â â + g ˆσ x (â + â ) (8) In our system, if we employ a new transformation Ĥ v = ˆV Ĥ ˆV + i d ˆV dt ˆV under ˆV = exp( iĥ 0v t/ ) where Ĥ 0v = 1 2 ω v ˆσ z + ν v â â is the free energy of the virtual trapped ion system. The resulting Hamiltonian in the interaction picture reads Ĥ v = 1 2 ω v ˆσ z + ν v â â + Ω[e iψ e i(ω l ω+δω)t ˆσ + e iψ e i(ω l ω+δω)t ˆσ + ] i Ωη 2 [âe i(ν δν)t + â e i(ν δν)t ] [e iψ e i(ω l ω+δω)t ˆσ + e iψ e i(ω l ω+δω)t ˆσ + ] Here, the virtual detuning parameters are detuned as δω = ω ω v and δν = ν ν v. For simplicity, we choose ψ = π 2 from now on. (CQI, IIIS, Tsinghua University, Beijing) Kihwan Kim s group September 7, / 15

9 For ω l = (ω δω) + (ν δν v ), we again get the anti-jcm-type Hamiltonian Ĥ 1 = 1 2 δωˆσ z + δνâ â + Ωη 2 (âˆσ + â ˆσ + ) (9) For ω l = (ω δω) (ν δν v ), we again get the JCM-type Hamiltonian Ĥ 2 = 1 2 δωˆσ z + δνâ â + Ωη 2 (âˆσ + + â ˆσ ) (10) Now we come to the time-evolution of a quantum state under the sum Ĥ 1 + Ĥ2 = δωˆσ z + 2 δνâ â + Ωη 2 ˆσ x(â + â ) (11) The striking similarity between the QRM Hamiltonian 8 and Eq. 11 leads to the interpretation of s pesudo effective atomic and trap frequency given by ω = 2δω, ω m = 2δν and g = ηω 2 (CQI, IIIS, Tsinghua University, Beijing) Kihwan Kim s group September 7, / 15

10 Spin and motion evolution at different coupling regime a g/ωm=04 b g/ωm=6 c g/ωm=2 g 8. p( ) n d e f time(μs) N =p( )+ n (CQI, IIIS, Tsinghua University, Beijing) Kihwan Kim s group September 7, / 15

11 Phonon bounce back and forth in the DSC regime for the degenerate ω 0 = 0 and non-degenerate case ω 0 0 case a c t=0μs t=10μs t=30μs p( ) p(n) b t=50μs t=70μs t=100μs p(n=0) p(n) time(μs) n (CQI, IIIS, Tsinghua University, Beijing) Kihwan Kim s group September 7, / 15

12 Adiabatically prepare the ground state in the DSC regime a ωm, g (MHz) time(μs) b p( ),purity time(μs) c g/ωm=2 d g/ωm=5 e g/ωm= Fidelity=89(02) Fidelity=87(03) 6 4 Fidelity=79(03) p(,n) p(,n) 1 05 Adiabaticity= n H/ t m /ΔEnm ωm g Adiabaticity n Ttarget Trevival (CQI, IIIS, Tsinghua University, Beijing) Kihwan Kim s group September 7, / 15

13 Energy spectrum Add modulate field that break the parity Ĥ modulate = ĤQRM + ggg Ωˆσ x (12) Ĥ modulate = ĤQRM + ggg Ωη(â + â ) (13) a 6 c 1 p( ) p( ) b (CQI, IIIS, Tsinghua University, Beijing) Kihwan Kim s group September 7, / 15 0

14 Group photos (CQI, IIIS, Tsinghua University, Beijing) Kihwan Kim s group September 7, / 15

15 Thanks for your attention! (CQI, IIIS, Tsinghua University, Beijing) Kihwan Kim s group September 7, / 15