7, Cavity Quantum ElectroDynamics (Cavity-QED) 1. Cavity Modes 2 ...

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Two-sided cavity a two-sided cavity has two partially transparent mirrors with associated loss coefficients γ1 and γ2, in this case there are two input ports and two output ports, the equation of motion for the internal field is d dt â(t) = −iω0â(t) − 1 2 (γ1 + γ2)â(t) + √ γ1âI(t) + √ γ2 ˆbI(t), the relationship between the internal and input field frequency components for an empty cavity is then √ γ1aI(ω) + a(ω) = √ γ2bI(ω) , − i(ω − ω0) γ1+γ2 2 IPT5340, Fall ’06 – p.16/23
Two-time correlation function two boundary conditions of the reservoir, ˆ b(ω) = e −iω(t−t0)ˆ b0(ω) + g(ω) ˆ b(ω) = e −iω(t−t1)ˆ b1(ω) − g(ω) the input and output fields, or âIN(t) = −1 √ 2π âOUT (t) = 1 √ 2π t dt ′ e −iω(t−t′ ) ′ â(t ), at time t0 < t, the input, t0 t1 t ∞ −∞ ∞ dt ′ e −iω(t−t′ ) â(t ′ ), at time t1 > t, the output, −∞ √ γ 1 âIN(t) = â(t) − √ 2 2π √ γ 1 âOUT (t) = â(t) + √ 2 2π dωe −iω(t−t0)ˆ b0(ω), dωe −iω(t−t1)ˆ b1(ω), dω ˆ b(ω, t), dω ˆ b(ω, t), IPT5340, Fall ’06 – p.17/23
Page 1 and 2: 7, Cavity Quantum ElectroDynamics (
Page 3 and 4: Field damping by field reservoirs c
Page 5 and 6: Field damping by field reservoirs t
Page 7 and 8: Cavity modes consider a single cavi
Page 9 and 10: Input-output theory the system oper
Page 11 and 12: d dt Input-output theory the system
Page 13 and 14: for a linear system where a(t) = d
Page 15: Linear system for example, consider
Page 19 and 20: Two-time correlation function let
Page 21 and 22: Quantum State Transfer as a Quantum
Page 23: Quantum State Transfer as a Quantum

7, Cavity Quantum ElectroDynamics (Cavity-QED) 1. Cavity Modes 2 ...

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