# Tensor in QuantumOptics

**URL:** <https://discourse.julialang.org/t/tensor-in-quantumoptics/125618>\
**Category:** Quantum\
**Created:** [February 6, 2025, 12:56pm UTC](https://discourse.julialang.org/t/tensor-in-quantumoptics/125618 "2025-02-06T12:56:58Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![gustave\_Robichon](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/gustave_robichon/32/207522_2.png) [@gustave\_Robichon](https://discourse.julialang.org/u/gustave_Robichon)\
**Post date:** [February 6, 2025, 12:56pm UTC](https://discourse.julialang.org/t/tensor-in-quantumoptics/125618/1 "2025-02-06T12:56:58Z")

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Hello 🙂  
I have a program using QuantumOptics. It uses several bosonic modes. While writing the Hamiltonian, I wonder if I should explictly use the tensor product : I[1] tensor I[2] tensor a[3] for exemple, instead of only a[3] ? Here is my code below 🙂 :

```julia
    n = 3
    Nmax = 50
    var_t = 0.125
    var_U = 0.125
    var_mu = 0.125

    basis = [FockBasis(Nmax) for i in 1:n]
    I = [identityoperator(basis[i]) for i in 1:n]
    a = [destroy(basis[i]) for i in 1:n]
    adag = [create(basis[i]) for i in 1:n]
    _number = [number(basis[i]) for i in 1:n]

    H = 0 * a[1]
    for i in 1:(n-1)
        #H += - var_t * ( b(i)' * b(i+1) + b(i) * b(i+1)' )
        H += -var_t * ( adag[i] * a[i+1] + adag[i+1] * a[i] )
    end

    for i in 1:n 
        #H += var_U/2.0 * (b(i)' * b(i)) * ( b(i)' * b(i)-1.0) - var_mu * b(i)'*b(i)
        H += var_U/2.0 * (_number[i] * (_number[i] - I[i] )) - var_mu * _number[i]
    end

```

is my code OK ? Thanks 🙂

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<div class="post-metadata">

**Author:** ![gustave\_Robichon](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/gustave_robichon/32/207522_2.png) [@gustave\_Robichon](https://discourse.julialang.org/u/gustave_Robichon)\
**Post date:** [February 12, 2025, 1:21pm UTC](https://discourse.julialang.org/t/tensor-in-quantumoptics/125618/2 "2025-02-12T13:21:23Z")

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Finally I use the following :

```julia
    basis = [FockBasis(Nmax) for i in 1:n]
    I = [identityoperator(basis[i]) for i in 1:n]
    _I = tensor(I...)
    a = [tensor( [ (i==j ? destroy(basis[i]) : I[j]) for j in 1:n ]... ) for i in 1:n] 
    adag = [tensor( [ (i==j ? create(basis[i]) : I[j]) for j in 1:n ]... ) for i in 1:n] 
    _number = [tensor( [ (i==j ? number(basis[i]) : I[j]) for j in 1:n ]... ) for i in 1:n]

    H = 0 * a[1]
    for i in 1:( n-1 )
        H += -var_t * ( adag[i] * a[i+1] + adag[i+1] * a[i] )
    end

    for i in 1:n 
        H += var_U/2.0 * ( _number[i] * (_number[i] - _I )) - var_mu * _number[i]
    end

    L = [var_epsilon * a[1] , var_epsilon * adag[n]]

```

I think it is OK !

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<div class="post-metadata">

**Author:** ![Krastanov](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/krastanov/32/6817_2.png) [@Krastanov](https://discourse.julialang.org/u/Krastanov)\
**Post date:** [February 12, 2025, 4:21pm UTC](https://discourse.julialang.org/t/tensor-in-quantumoptics/125618/3 "2025-02-12T16:21:06Z")

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I think the `embed` function would make your life much easier. It is the main tool to use when you want to move from a subsystem Hamiltonian (e.g. for a given harmonic oscillator) to a Hamiltonian for the entire system (e.g. multiple modes).