prueba_laser_squeezed.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Squeezed Lasing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qutip import *\n",
    "import math as math\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib as mpl\n",
    "from matplotlib import cm\n",
    "import scipy as scipy\n",
    "import matplotlib.animation as animation\n",
    "from tqdm import tqdm\n",
    "import sys\n",
    "import matplotlib.colors as colors\n",
    "import matplotlib.gridspec as gridspec\n",
    "import os"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Definition of parameters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bare parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 350 # Dimension of the Hilbert space of the cavity\n",
    "g_0 = 1 # light-matter coupling\n",
    "n_q = 50 # Photon saturation number\n",
    "C = np.linspace(1e-15,2,100) # Cooperativity (equal to the pumping parameter p)\n",
    "k = g_0*np.sqrt(2/(C*n_q)) # Photon decay rate\n",
    "P = 2*n_q*k # Incoherent pumping\n",
    "eta = np.zeros(np.size(C)) # Photon loss due to other decay channels\n",
    "omega_p = 1 # Amplitude of the coherent drive (down-conversion)\n",
    "delta_c = 1 # Detuning w_c-w_p\n",
    "delta_sigma = 1 # Detuning w_sigma-w_p"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Squeezed parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "r = 1 # Squeezing parameter\n",
    "theta = np.pi # Squeezing angle\n",
    "delta_s = delta_c*np.sqrt(1-(omega_p/delta_c)**2) # Detuning in the squeezed basis\n",
    "C_s = C*np.cosh(r)**2 # Squeezed cooperativity (equal to the squeezed pumping parameter p_s)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Check RWA condition $\\Delta_\\sigma, \\Delta_s >> g\\sinh{r}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Check values of delta_c and omega_p\n",
      "1.1752011936438014\n"
     ]
    }
   ],
   "source": [
    "aux = 2\n",
    "\n",
    "if delta_sigma > aux*g_0*np.sinh(r):\n",
    "    if delta_s > aux*g_0*np.sinh(r):\n",
    "        print('double check')\n",
    "    else:\n",
    "        print('Check values of delta_c and omega_p')\n",
    "else:\n",
    "    print('Check values of delta_c and omega_p')\n",
    "print(g_0*np.sinh(r))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Definition of operators"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Gain medium (1 atom $\\rightarrow$ two-level system)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "g = basis(2,0) # Ground state\n",
    "e = basis(2,1) # Excited state\n",
    "sigma = tensor(identity(N),g*e.dag()) # Lowering operator"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Annihilation operator in the squeezed basis $\\hat{a}_s$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "a_s = tensor(destroy(N),identity(2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Annihilation operator in the bare basis $\\hat{a}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = a_s*np.cosh(r)-np.exp(-1j*theta)*a_s.dag()*np.sinh(r)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Squeezing operator $S(\\xi)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "chi = r*np.exp(-1j*theta) \n",
    "S = (0.5*(chi*a*a-np.conj(chi)*a.dag()*a.dag())).expm() # Squeezing operator"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Hamiltonian in the squeezed basis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "H = delta_s*a_s.dag()*a_s+delta_sigma*sigma.dag()*sigma+g_0*np.cosh(r)*(a_s.dag()*sigma+a_s*sigma.dag())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Stationary state of the system"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solving the master equation for $\\rho_s$ and different values of $C$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  0%|          | 0/100 [00:00<?, ?it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 100/100 [02:29<00:00,  1.49s/it]\n"
     ]
    }
   ],
   "source": [
    "result = [] # Steady states of the system in the squeezed basis\n",
    "\n",
    "for i in tqdm(range(np.size(C))):    \n",
    "    coll1 = np.sqrt(P[i])*sigma.dag() # Collapse operator for incoherent pumping\n",
    "    coll2 = np.sqrt(k[i]*(1+eta[i]))*a_s # Collapse operator for photon decay\n",
    "    result.append(steadystate(H, [coll1,coll2]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Return to bare basis $\\rho$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "bare_rho = S*result*S.dag() # Steady states in the bare basis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Photon population and lasing threshold"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_s = np.zeros(np.size(C)) # Photon population in the squeezed basis\n",
    "\n",
    "for i in range(np.size(C)):   \n",
    "    n_s[i] = expect(a_s.dag()*a_s,result[i])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Mean-field solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "mfs = np.heaviside(C_s-1,0)*n_q*(1-1/C_s)*np.cosh(2*r)+np.sinh(r)**2 # Mean-field solution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Photon population in the bare basis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = n_s*np.cosh(2*r)+np.sinh(r)**2 # Photon population"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Check that $\\langle \\hat{a}_s^2\\rangle$ and $\\langle\\hat{a}_s^{\\dag 2}\\rangle$ are zero"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0j\n"
     ]
    }
   ],
   "source": [
    "exp_as = np.zeros(np.size(C),dtype=np.complex_) # Expected value of a_s^2\n",
    "exp_asd = np.zeros(np.size(C),dtype=np.complex_) # Expected value of a_s.dag^2\n",
    "for i in range(np.size(C)):   \n",
    "    exp_as[i] = expect(a_s**2,result[i])\n",
    "    exp_asd[i] = expect(a_s.dag()**2,result[i])\n",
    "print(np.sum(exp_as+exp_asd))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plot photon number $n$ against $C$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x225e9990d60>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(C,n,label='Numerical result')\n",
    "plt.plot(C,mfs,'--', label='Mean-field result')\n",
    "plt.xlim([np.min(C),np.max(C)])\n",
    "plt.ylim([0,2*n_q])\n",
    "plt.title('Photon number ($r=$'+str(r)+')',fontsize=14)\n",
    "plt.xlabel('C',fontsize=14)\n",
    "plt.ylabel('n',fontsize=14)\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\"> \n",
    "<b>Note: </b>From this point onwards the cooperativity value is chosen always to be 1."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Wigner function of the phase-diffused steady-state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "wig_xvec = np.linspace(-25,25,100) # Values of x in the phase space\n",
    "wig_pvec = np.linspace(-10,10,100) # Values of p in the phase space (squeezed quadrature)\n",
    "index = 50 # Index of the cooperativity value\n",
    "Wigner = wigner(bare_rho[index].ptrace(0),wig_xvec,wig_pvec) # Calculation of the Wigner function for C[index]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'p')"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nrm = mpl.colors.Normalize(-Wigner.max(),Wigner.max()) # Colorbar settings\n",
    "cbar = plt.colorbar(cm.ScalarMappable(norm=nrm, cmap=cm.RdBu_r))\n",
    "cbar.set_label('W(x,p)',fontsize=14)\n",
    "\n",
    "plt.contourf(wig_xvec, wig_pvec, Wigner, 100, cmap=cm.RdBu_r, norm=nrm) # Plot of the Wigner\n",
    "\n",
    "plt.xlim([np.min(wig_xvec),np.max(wig_xvec)]) # Figure settings\n",
    "plt.ylim([np.min(wig_pvec),np.max(wig_pvec)])\n",
    "plt.title('Steady state Wigner function ($r=$'+str(r)+', $C=$'+str(format(C[index],'.1f'))+')',fontsize=14)\n",
    "plt.axis('scaled')\n",
    "plt.xlabel('x',fontsize=14)\n",
    "plt.ylabel('p',fontsize=14)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Emission spectrum $S(\\omega)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Time vector in terms of the cavity caracteristic decay time $\\kappa$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "tau_vec = np.linspace(0,100/k[index],500) # Time vector of delays"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Collapse operators for parameters corresponding to $C=1$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "coll1_C = np.sqrt(P[index])*sigma.dag() # Collapse operator for incoherent pumping\n",
    "coll2_C = np.sqrt(k[index]*(1+eta[index]))*a_s # Collapse operator for photon decay"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Computation of the emission spectrum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 100/100 [00:50<00:00,  1.98it/s]\n"
     ]
    }
   ],
   "source": [
    "L = [] # Liouvillian\n",
    "vp = [] # Eigenvalues of the Liouvillian\n",
    "for i in tqdm(range(np.size(C))):   \n",
    "    L.append(liouvillian(H, [coll1_C,coll2_C]))\n",
    "    #vp.append(L[i].eigenenergies())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "corr = correlation_2op_1t(H, None, tau_vec, [coll1_C,coll2_C], a.dag(), a)\n",
    "wlist, spec = spectrum_correlation_fft(tau_vec,corr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "check = np.zeros(np.size(tau_vec))\n",
    "for i in range(np.size(tau_vec)):\n",
    "    check[i] = np.abs(spec[i])-np.abs(spec[-i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.1, 0.1)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(wlist/(2*np.pi),spec)\n",
    "plt.title('freq. spectrum',fontsize=14)\n",
    "plt.xlabel('$\\omega$',fontsize=14)\n",
    "plt.xlim([-0.1,0.1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Secord order coherence function $g^{(2)}(\\tau)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "corr2 = correlation_3op_1t(H, None, tau_vec, [coll1_C,coll2_C], a.dag(), a.dag()*a, a)\n",
    "n_corr = mesolve(H, result[index], tau_vec, [coll1_C,coll2_C], [a.dag()*a]).expect[0]\n",
    "corr_2f = corr2/(n_corr[0]*n_corr[np.size(tau_vec)-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Second order coherence function')"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(tau_vec*k[index],np.real(corr_2f))\n",
    "plt.plot([0,101],[1,1],'--',lw=0.5,color='k')\n",
    "plt.ylim([0,2])\n",
    "plt.xlim(0.1,100)\n",
    "plt.xlabel(r'$\\tau\\kappa$',fontsize=14)\n",
    "plt.ylabel(r'$g^{(2)}(\\tau)$',fontsize=14)\n",
    "plt.semilogx()\n",
    "plt.title('Second order coherence function',fontsize=14)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## More things (to be done...)\n",
    "- Symmetry broken solutions\n",
    "- Squeezed spectrum\n",
    "- Relation between $\\eta$ and $N_s$"
   ]
  }
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