API Reference

SLH(name, inputs, outputs, S, L, H)

An SLH triple describes an open quantum system. See Combes, arXiv.1611.00375

The name of the system should be unique. When multiple systems are combined, the names of their inputs and outputs will have the system name appended to them. The inputs and outputs describe 'ports' where signals leave and enter the system. Quantum systems must have the same number of inputs and outputs, which we denote by n.

size(S) = (n, n) <- S is an nxn matrix

size(L) = (n,)

size(H) = ()

The two ways of combining SLH systems are concatenate() and feedbackreduce()

concatenate(name, syslist::Vector{SLH})

creates a composite system with no interconnections. Combes eq. 59

When systems are concatenated, the names of their inputs, outputs, operators, parameters, and Hilbert spaces are 'promoted' by prepending the name of the system to the existing name. This prevents name collisions as long as all SLHSystems are created with a unique name.

feedbackreduce(A::SLH,output,input)

Connects the output port to the input port, reducing the number of outputs and inputs by one each. Combes eq 61.

operators(sys)

returns all the quantum operators contained in the system's Hamiltonian.

parameters(sys)

returns all the symbolic numbers contained in the system's Hamiltonian and coupling vector L.

get_qnumbers(expr)

Extract all quantum operators from an expression.

Arguments

• expr: A symbolic expression

Returns

• Set: Set of quantum operators found in the expression

get_numsymbols(expr)

Extract all symbolic parameters from an expression.

Arguments

• expr: A symbolic expression

Returns

• Set: Set of symbolic parameters found in the expression

get_additive_terms(expr)

Extract additive terms from a quantum operator expression.

Takes an expression containing quantum operators and returns a list of terms that contain no addition, only multiplication. Summing all returned terms results in the original expression.

Arguments

• expr: A symbolic expression containing quantum operators

Returns

• Vector: List of terms without addition operators

cavity(name)

Create a basic optical cavity SLH system.

Creates a single-mode cavity with detuning and decay. The cavity has one input and one output port with direct transmission (S=1).

Arguments

• name: Symbol identifying the cavity (used for operator and parameter naming)

Returns

• SLH: System with Hamiltonian H = Δ·a†a and coupling L = [√κ·a]

Parameters

• κ: Cavity decay rate
• Δ: Cavity detuning from driving field

squeezing_cavity(name)

Create a squeezing cavity SLH system.

Creates a cavity that generates squeezed light through a parametric interaction (two-mode squeezing Hamiltonian).

Arguments

• name: Symbol identifying the cavity (used for operator and parameter naming)

Returns

• SLH: System with squeezing Hamiltonian H = iϵ(a†² - a²) and coupling L = [√κ·a]

Parameters

• κ: Cavity decay rate
• ϵ: Squeezing strength

radiation_pressure_cavity(name)

Create an optomechanical cavity with radiation pressure coupling.

Creates a two-mode system with an optical cavity mode coupled to a mechanical oscillator through radiation pressure.

Arguments

• name: Symbol identifying the system (used for operator and parameter naming)

Returns

• SLH: Optomechanical system with optical and mechanical modes

Parameters

• κ: Cavity decay rate
• Δ: Cavity detuning
• Ω: Mechanical frequency
• g: Optomechanical coupling strength

qed_cavity(name)

Create a cavity QED system with a two-level atom.

Creates a cavity containing a two-level atom with Jaynes-Cummings coupling and an external driving field.

Arguments

• name: Symbol identifying the system (used for operator and parameter naming)

Returns

• SLH: System with cavity-atom interaction and driving

Parameters

• Δ: Cavity detuning
• g: Atom-cavity coupling strength
• κ: Cavity decay rate
• h: External driving amplitude