Entanglement Evolution Characteristics of Quantum Rabi Models with Two Arbitrary Qubits

Yuhu Xu; Xuezao Ren; Xueying Liu

doi:10.3788/AOS201838.0127001

Journals >Acta Optica Sinica >Volume 38 >Issue 1 >Page 0127001 > Article

Acta Optica Sinica
Vol. 38, Issue 1, 0127001 (2018)

Entanglement Evolution Characteristics of Quantum Rabi Models with Two Arbitrary Qubits

Yuhu Xu, Xuezao Ren^*, and Xueying Liu

Author Affiliations

School of Science, Southwest University of Science and Technology, Mianyang, Sichuan 621010, China

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DOI: 10.3788/AOS201838.0127001 Cite this Article Set citation alerts

Yuhu Xu, Xuezao Ren, Xueying Liu. Entanglement Evolution Characteristics of Quantum Rabi Models with Two Arbitrary Qubits[J]. Acta Optica Sinica, 2018, 38(1): 0127001 Copy Citation Text

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Fig. 1. Concurrent entanglement evolution of identical qubits. (a) g1=g2=0.01, ω0=1; (b) g1=g2=0.1, ω0=1

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Fig. 2. Concurrent entanglement evolution of non-identical qubits. (a) g1=g2=0.01; (b) g1=g2=0.1

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Fig. 3. Concurrent entanglement evolution when resonance between non-identical qubits and light field occurs (ω1=ω2=ω0, g2=0.01)

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Wave function		$\begin{matrix} ψ_{(E_{1,0}^{-})} \end{matrix}$	$\begin{matrix} ψ_{(E_{2,0}^{-})} \end{matrix}$	$\begin{matrix} ψ_{(E_{2,0}^{+})} \end{matrix}$	$\begin{matrix} ψ_{(E_{1,1}^{-})} \end{matrix}$	$\begin{matrix} ψ_{(E_{1,0}^{+})} \end{matrix}$	$\begin{matrix} ψ_{(E_{2,1}^{-})} \end{matrix}$	$\begin{matrix} ψ_{(E_{2,1}^{+})} \end{matrix}$	$\begin{matrix} ψ_{(E_{1,2}^{-})} \end{matrix}$
ω₁=ω₂=0.9	$\begin{matrix} E_{j, m}^{\pm} \end{matrix}$	-0.900105	-0.002069	0	0.101753	0.897999	0.998001	1.000000	1.103579
ω₁=ω₂=0.9	$\begin{matrix} k_{j, m}^{\pm} \end{matrix}$	-2.57×10^-16	-0.990471	8.82×10^-14	-0.137522	2.92×10^-17	1.17×10^-16	-2.04×10^-16	-4.05×10^-16
ω₁=ω₂=1.1	$\begin{matrix} E_{j, m}^{\pm} \end{matrix}$	-1.100095	0.001865	0	-0.102150	1.101997	1.000000	1.001787	0.895834
ω₁=ω₂=1.1	$\begin{matrix} k_{j, m}^{\pm} \end{matrix}$	-6.57×10^-16	-0.990512	1.55×10^-13	-0.137262	-3.48×10^-16	-1.72×10^-17	1.31×10^-16	-2.81×10^-16

Table 1. Energy spectra and coefficients of corresponding eigen-wavefunctions in entanglement evolution process of qubits when g1=g2=0.01

Wave function		$\begin{matrix} ψ_{(E_{1,0}^{-})} \end{matrix}$	$\begin{matrix} ψ_{(E_{2,0}^{-})} \end{matrix}$	$\begin{matrix} ψ_{(E_{2,0}^{+})} \end{matrix}$	$\begin{matrix} ψ_{(E_{1,1}^{-})} \end{matrix}$	$\begin{matrix} ψ_{(E_{1,0}^{+})} \end{matrix}$	$\begin{matrix} ψ_{(E_{2,1}^{-})} \end{matrix}$	$\begin{matrix} ψ_{(E_{2,1}^{+})} \end{matrix}$	$\begin{matrix} ψ_{(E_{1,2}^{-})} \end{matrix}$
ω₁=ω₂=0.9	$\begin{matrix} E_{j, m}^{\pm} \end{matrix}$	-0.910701	-0.114551	0	0.182685	0.742299	0.958553	1.000000	1.256710
ω₁=ω₂=0.9	$\begin{matrix} k_{j, m}^{\pm} \end{matrix}$	4.37×10^-15	0.803694	1.08×10^-15	-0.590504	-7.36×10^-16	8.93×10^-16	6.09×10^-16	9.71×10^-16
ω₁=ω₂=1.1	$\begin{matrix} E_{j, m}^{\pm} \end{matrix}$	-0.900105	0.101753	0	-0.002069	0.897999	1.103579	1.000000	0.897999
ω₁=ω₂=1.1	$\begin{matrix} k_{j, m}^{\pm} \end{matrix}$	2.48×10^-15	-0.823362	6.53×10^-15	0.563598	7.47×10^-16	-1.55×10^-15	-3.86×10^-16	-7.02×10^-16

Table 2. Energy spectra and coefficients of corresponding eigen-wavefunctions in entanglement evolution process of qubits when g1=g2=0.1

Wave function		$\begin{matrix} ψ_{(E_{1,0}^{-})} \end{matrix}$	$\begin{matrix} ψ_{(E_{2,0}^{-})} \end{matrix}$	$\begin{matrix} ψ_{(E_{1,1}^{-})} \end{matrix}$	$\begin{matrix} ψ_{(E_{2,0}^{+})} \end{matrix}$	$\begin{matrix} ψ_{(E_{2,1}^{-})} \end{matrix}$	$\begin{matrix} ψ_{(E_{1,0}^{+})} \end{matrix}$	$\begin{matrix} ψ_{(E_{1,2}^{-})} \end{matrix}$	$\begin{matrix} ψ_{(E_{2,1}^{+})} \end{matrix}$
Δω=0.1ω₁=1.1ω₂=0.9	$\begin{matrix} E_{j, m}^{\pm} \end{matrix}$	-1.000100	-0.101045	-0.000197	0.100941	0.896995	0.999711	1.000000	1.102893
Δω=0.1ω₁=1.1ω₂=0.9	$\begin{matrix} k_{j, m}^{\pm} \end{matrix}$	7.43×10^-16	0.707258	0.000275	0.706920	-2.66×10^-15	1.87×10^-16	-1.28×10^-15	8.39×10^-16
Δω=0.2ω₁=1.2ω₂=0.8	$\begin{matrix} E_{j, m}^{\pm} \end{matrix}$	-1.000101	-0.200545	-0.000201	0.200443	0.798469	0.999700	1.000000	1.201427
Δω=0.2ω₁=1.2ω₂=0.8	$\begin{matrix} k_{j, m}^{\pm} \end{matrix}$	-1.65×10^-16	0.707179	-0.000071	0.706999	4.53×10^-16	-1.41×10^-16	1.24×10^-16	-1.45×10^-16
Δω=0.3ω₁=1.3ω₂=0.7	$\begin{matrix} E_{j, m}^{\pm} \end{matrix}$	-1.000102	-0.300377	-0.000204	0.300274	0.698973	0.999694	1.000000	1.300924
Δω=0.3ω₁=1.3ω₂=0.7	$\begin{matrix} k_{j, m}^{\pm} \end{matrix}$	-2.19×10^-15	0.707151	0.000032	0.707026	-9.45×10^-16	-1.21×10^-15	4.68×10^-15	1.19×10^-15

Table 3. Energy spectra and coefficients of corresponding eigen-wavefunctions under different detunings in entanglement evolution process of qubits

Wave function		$\begin{matrix} ψ_{(E_{1,0}^{-})} \end{matrix}$	$\begin{matrix} ψ_{(E_{2,0}^{-})} \end{matrix}$	$\begin{matrix} ψ_{(E_{1,1}^{-})} \end{matrix}$	$\begin{matrix} ψ_{(E_{2,0}^{+})} \end{matrix}$	$\begin{matrix} ψ_{(E_{1,0}^{+})} \end{matrix}$	$\begin{matrix} ψ_{(E_{1,2}^{-})} \end{matrix}$	$\begin{matrix} ψ_{(E_{2,1}^{+})} \end{matrix}$	$\begin{matrix} ψ_{(E_{1,2}^{-})} \end{matrix}$
g₁=0.05	$\begin{matrix} E_{j, m}^{\pm} \end{matrix}$	-1.001301	-0.052379	-0.001108	0.049583	0.922242	0.954430	1.043357	1.074762
g₁=0.05	$\begin{matrix} k_{j, m}^{\pm} \end{matrix}$	-2.41×10^-15	-0.584903	0.554360	-0.591713	-2.07×10^-15	1.75×10^-15	2.95×10^-16	9.42×10^-16
g₁=0.1	$\begin{matrix} E_{j, m}^{\pm} \end{matrix}$	-1.005064	-0.105560	-0.004863	0.095208	0.850272	0.898578	1.091787	1.139009
g₁=0.1	$\begin{matrix} k_{j, m}^{\pm} \end{matrix}$	2.38×10^-15	-0.538020	0.632066	-0.556330	-1.25×10^-15	-3.51×10^-15	2.28×10^-15	-2.41×10^-15
g₁=0.2	$\begin{matrix} E_{j, m}^{\pm} \end{matrix}$	-1.020257	-0.219764	-0.020047	0.178612	0.697245	0.782677	1.176945	1.260329
g₁=0.2	$\begin{matrix} k_{j, m}^{\pm} \end{matrix}$	3.55×10^-15	-0.502236	0.666685	-0.545469	1.63×10^-15	-3.36×10^-15	1.00×10^-15	5.56×10^-16

Table 4. Energy spectra and coefficients of corresponding eigen-wavefunctions in entanglement evolution process of qubits under different g1 value (g2=0.01)

Yuhu Xu, Xuezao Ren, Xueying Liu. Entanglement Evolution Characteristics of Quantum Rabi Models with Two Arbitrary Qubits[J]. Acta Optica Sinica, 2018, 38(1): 0127001

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