coherent.m
Coherent state of a bosonic mode. Builds the normalised truncation of the coherent state with the specified amplitude on the specified bosonic mode, with unit operators on all other particles of the system. The Fock state amplitudes are the usual Poissonian coefficients, alpha^n/sqrt(n!), taken up to the truncation level of the mode declared in sys.isotopes; because the truncation chops the tail of the Poisson distribution, the state is renormalised afterwards and the norm lost to the truncation is reported to the console. That number is a convergence diagnostic: if it is not small, the mode needs more levels.
The output is a density matrix in Hilbert space formalisms and its vectorisation in Liouville space formalisms, in the same way as state.m and equilibrium.m behave.
Syntax
rho=coherent(spin_system,mode,alpha)
Parameters
mode - index of a bosonic mode in sys.isotopes
alpha - coherent state amplitude, a complex scalar
Outputs
rho - coherent state density matrix (zeeman-hilb)
or its vectorisation (zeeman-liouv)
Examples
A five-level resonator prepared in a coherent state of amplitude 1.5, propagated under amplitude damping:
% Microwave resonator with five Fock levels
sys.isotopes={'C5'};
inter.modes.frqs={6.02e9};
inter.modes.lifetimes={10e-9};
inter.temperature=0.050;
% Coherent state of the mode
rho=coherent(spin_system,1,1.5);
Notes
- The Fock space truncation of the mode chops the tail of the Poisson distribution; the state is renormalised after the truncation and the lost weight is reported.
- A coherent state of amplitude alpha has a mean population of |alpha|^2, so the truncation should leave several levels above that number.
See also
state.m, operator.m, equilibrium.m, weyl.m, rlx_modes.m, device.m, Spin system specification, Kernel functions
Version 2.12, authors: Ilya Kuprov
