591 lines
238 KiB
Plaintext
591 lines
238 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 81,
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"metadata": {},
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"outputs": [],
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"source": [
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"from sympy.functions.special.error_functions import erf\n",
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"from fewfermions.simulate.numerics import discrete_hamiltonian\n",
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"from scipy import sparse"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 110,
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"metadata": {},
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"outputs": [],
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"source": [
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"from helpers_merging import *\n",
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"\n",
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"initial_power = 100* si.uW\n",
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"initial_waist = 1.1*si.uW\n",
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"initial_distance = 4*si.um\n",
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"\n",
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"trap: DoubleTweezer = DoubleTweezer(\n",
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" power=0, # Set pancake laser power to 0, no 2D trap\n",
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" grad_z= 0*si.G/si.cm,\n",
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" grad_r=0,\n",
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" power_tweezer1 = initial_power,\n",
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" power_tweezer2 = initial_power,\n",
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" waist_tweezer1 = initial_waist,\n",
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" waist_tweezer2 = initial_waist,\n",
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" distance_tweezers = initial_distance,\n",
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"\n",
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" a=180*(4 * np.pi * const.epsilon_0 * const.value(\"Bohr radius\")**3)/(2 * const.epsilon_0 * const.c),\n",
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" wvl = 532 * si.nm,\n",
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"\n",
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" g = 0,\n",
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")\n",
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"\n",
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"left_cutoff = -0.5*initial_distance-3*float(trap.subs(trap.waist_tweezer1))\n",
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"right_cutoff = 0.5*initial_distance+3*float(trap.subs(trap.waist_tweezer2))\n",
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"\n",
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"x, y, z = trap.x, trap.y, trap.z"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 111,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/latex": [
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"$\\displaystyle a \\left(\\frac{2 P_{t1} e^{- \\frac{d_{t}^{2}}{2 W_{t1}^{2}}}}{\\pi W_{t1}^{2}} + \\frac{2 P_{t2} e^{- \\frac{d_{t}^{2}}{2 W_{t2}^{2}}}}{\\pi W_{t2}^{2}}\\right) - a \\left(\\frac{2 P_{t1} e^{\\frac{- 2 y^{2} - 2 \\left(\\frac{d_{t}}{2} + x\\right)^{2}}{W_{t1}^{2} \\left(1 + \\frac{\\lambda^{2} z^{2}}{\\pi^{2} W_{t1}^{4}}\\right)}}}{\\pi W_{t1}^{2} \\left(1 + \\frac{\\lambda^{2} z^{2}}{\\pi^{2} W_{t1}^{4}}\\right)} + \\frac{2 P_{t2} e^{\\frac{- 2 y^{2} - 2 \\left(- \\frac{d_{t}}{2} + x\\right)^{2}}{W_{t2}^{2} \\left(1 + \\frac{\\lambda^{2} z^{2}}{\\pi^{2} W_{t2}^{4}}\\right)}}}{\\pi W_{t2}^{2} \\left(1 + \\frac{\\lambda^{2} z^{2}}{\\pi^{2} W_{t2}^{4}}\\right)}\\right) - g m z$"
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],
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"text/plain": [
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"a*(2*P_t1*exp(-d_t**2/(2*W_t1**2))/(pi*W_t1**2) + 2*P_t2*exp(-d_t**2/(2*W_t2**2))/(pi*W_t2**2)) - a*(2*P_t1*exp((-2*y**2 - 2*(d_t/2 + x)**2)/(W_t1**2*(1 + lambda**2*z**2/(pi**2*W_t1**4))))/(pi*W_t1**2*(1 + lambda**2*z**2/(pi**2*W_t1**4))) + 2*P_t2*exp((-2*y**2 - 2*(-d_t/2 + x)**2)/(W_t2**2*(1 + lambda**2*z**2/(pi**2*W_t2**4))))/(pi*W_t2**2*(1 + lambda**2*z**2/(pi**2*W_t2**4)))) - g*m*z"
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]
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},
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"execution_count": 111,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"trap.get_potential().subs({trap.power:0,trap.grad_z:0, trap.grad_r:0})"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 112,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/latex": [
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"$\\displaystyle - \\frac{9.24016432665953 \\cdot 10^{-29} e^{- 1652892561983.47 \\left(x + 2.0 \\cdot 10^{-6}\\right)^{2}}}{\\pi} - \\frac{9.24016432665953 \\cdot 10^{-29} e^{- 1652892561983.47 \\left(x - 2.0 \\cdot 10^{-6}\\right)^{2}}}{\\pi}$"
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],
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"text/plain": [
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"-9.24016432665953e-29*exp(-1652892561983.47*(x + 2.0e-6)**2)/pi - 9.24016432665953e-29*exp(-1652892561983.47*(x - 2.0e-6)**2)/pi"
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]
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},
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"execution_count": 112,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"trap.subs(trap.get_potential(apply_zero_offset=False)).subs({y:0,z:0})"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 113,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 500x500 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"trap[trap.distance_tweezers] = initial_distance\n",
|
|
"plot_solutions(trap,2,left_cutoff,right_cutoff,display_plot=-1,state_mult=40,n_pot_steps=2000,plot=True,ret_results=False)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 114,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
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"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"n_levels=10\n",
|
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"n_pot_steps=2000\n",
|
|
"x_np = np.linspace(left_cutoff,right_cutoff,n_pot_steps)\n",
|
|
"\n",
|
|
"distances = np.linspace(0*si.um,initial_distance,500)\n",
|
|
"energies = np.zeros((len(distances),n_levels))\n",
|
|
"states = np.zeros((len(distances),n_levels,n_pot_steps))\n",
|
|
"potential = np.zeros((len(distances),n_pot_steps))\n",
|
|
"\n",
|
|
"#diagonalise hamiltonian for all distances\n",
|
|
"for i, dist in enumerate(distances):\n",
|
|
" trap[trap.distance_tweezers] = dist\n",
|
|
" num, ener, state, pot = plot_solutions(trap,n_levels,np.min(x_np),np.max(x_np),display_plot=0,state_mult=450,n_pot_steps=n_pot_steps,plot=False,ret_results=True)\n",
|
|
" energies[i,:len(ener)] = ener\n",
|
|
" states[i,:len(ener)] = state\n",
|
|
" potential[i] = pot(x_np)\n",
|
|
"\n",
|
|
"\n",
|
|
"#plot eigenenergies\n",
|
|
"plt.axvline(float(trap.subs(trap.waist_tweezer1))/si.um, color=\"black\",label=\"tweezer waist\")\n",
|
|
"for i in range(n_levels):\n",
|
|
" plt.plot(distances/si.um,energies[:,i],label=f\"state {i}\")\n",
|
|
"\n",
|
|
"plt.title(\"Eigenenergies of lowest states at different tweezer distances\")\n",
|
|
"plt.xlabel(\"tweezer distance [um]\")\n",
|
|
"plt.ylabel(\"energy [a.u.]\")\n",
|
|
"\n",
|
|
"plt.grid()\n",
|
|
"plt.legend()\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 108,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/latex": [
|
|
"$\\displaystyle - \\frac{1139835.08686124 a \\left(P_{t1} W_{t2} \\left(\\operatorname{erf}{\\left(\\frac{1.4142135623731 x}{W_{t1}} \\right)} + \\operatorname{erf}{\\left(\\frac{4.94974746830583 \\cdot 10^{-7} - 1.41421356237309 x}{W_{t1}} \\right)}\\right) + P_{t2} W_{t1} \\left(- \\operatorname{erf}{\\left(\\frac{1.4142135623731 x}{W_{t2}} \\right)} + \\operatorname{erf}{\\left(\\frac{1.41421356237309 x + 4.94974746830583 \\cdot 10^{-7}}{W_{t2}} \\right)}\\right)\\right)}{W_{t1} W_{t2}}$"
|
|
],
|
|
"text/plain": [
|
|
"-1139835.08686124*a*(P_t1*W_t2*(erf(1.4142135623731*x/W_t1) + erf((4.94974746830583e-7 - 1.41421356237309*x)/W_t1)) + P_t2*W_t1*(-erf(1.4142135623731*x/W_t2) + erf((1.41421356237309*x + 4.94974746830583e-7)/W_t2)))/(W_t1*W_t2)"
|
|
]
|
|
},
|
|
"execution_count": 108,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"-trap.a*np.sqrt(2/np.pi)/initial_distance/trap.waist_tweezer1/trap.waist_tweezer2* (trap.power_tweezer1*trap.waist_tweezer2*(erf((initial_distance-2*x)/np.sqrt(2)/trap.waist_tweezer1) +\n",
|
|
" erf(np.sqrt(2)*x/trap.waist_tweezer1))\n",
|
|
" + trap.power_tweezer2*trap.waist_tweezer1*(erf((initial_distance+2*x)/np.sqrt(2)/trap.waist_tweezer2) -\n",
|
|
" erf(np.sqrt(2)*x/trap.waist_tweezer2)))"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 109,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"#calculate average potential as tweezer distance is decreased from \"initial_distance\" to zero\n",
|
|
"average_pot = sp.lambdify(x,trap.subs(-trap.a*np.sqrt(2/np.pi)/initial_distance/trap.waist_tweezer1/trap.waist_tweezer2* (trap.power_tweezer1*trap.waist_tweezer2*(erf((initial_distance-2*x)/np.sqrt(2)/trap.waist_tweezer1) +\n",
|
|
" erf(np.sqrt(2)*x/trap.waist_tweezer1))\n",
|
|
" + trap.power_tweezer2*trap.waist_tweezer1*(erf((initial_distance+2*x)/np.sqrt(2)/trap.waist_tweezer2) -\n",
|
|
" erf(np.sqrt(2)*x/trap.waist_tweezer2)))))\n",
|
|
"\n",
|
|
"#average_pot = sp.lambdify(y,trap.subs(-trap.a*np.sqrt(2/np.pi)/initial_distance*((trap.power_tweezer1/trap.waist_tweezer1*erf((initial_distance-2*y)/np.sqrt(2)/trap.waist_tweezer1)) +\n",
|
|
"# (trap.power_tweezer2/trap.waist_tweezer2*erf((initial_distance+2*y)/np.sqrt(2)/trap.waist_tweezer2)))))\n",
|
|
"average_potential = average_pot(x_np)\n",
|
|
"#plt.plot(x_np,average_potential)\n",
|
|
"\n",
|
|
"#get the time averaged hamiltonian\n",
|
|
"dx = np.mean(np.diff(x_np))\n",
|
|
"mean_ham = discrete_hamiltonian(dx,average_potential,float(trap.subs(trap.m).evalf()))\n",
|
|
"mean_ham_square = mean_ham**2\n",
|
|
"\n",
|
|
"#compute the time \"tau\" needed to make it an adiabatic process\n",
|
|
"delta_ham = np.zeros(n_levels)\n",
|
|
"for i in range(n_levels):\n",
|
|
" delta_ham[i] = np.sqrt(states[-1,i].dot(mean_ham_square.dot(states[-1,i]))-(states[-1,i].dot(mean_ham.dot(states[-1,i])))**2)\n",
|
|
"tau = const.hbar/delta_ham\n",
|
|
"\n",
|
|
"\"\"\"\n",
|
|
"plt.plot(tau/si.us,\"o\")\n",
|
|
"plt.xlabel(\"state number []\")\n",
|
|
"plt.ylabel(\"time [us]\")\n",
|
|
"plt.title(\"time needed for adiabatic process\")\"\"\"\n",
|
|
"\n",
|
|
"\n",
|
|
"plt.plot(initial_distance/si.cm/tau,\"o\")\n",
|
|
"plt.xlabel(\"state number []\")\n",
|
|
"plt.ylabel(\"velocity [cm/s]\")\n",
|
|
"plt.title(\"average velocity for adiabatic process\")\n",
|
|
"\n",
|
|
"plt.grid()\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Calculate time interval for adiabatic transition"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 89,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"dx = np.mean(np.diff(x_np))"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 90,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"n_levels = 10\n",
|
|
"\n",
|
|
"mean_ham = 0\n",
|
|
"for i, dist in enumerate(distances):\n",
|
|
" mean_ham += discrete_hamiltonian(dx,potential[i],float(trap.subs(trap.m).evalf()))\n",
|
|
"\n",
|
|
"\n",
|
|
"eigenvals, eigenvects = sparse.linalg.eigsh(mean_ham, k=n_levels, which=\"LM\", sigma=np.min(potential))\n",
|
|
"eigenvals_square, eigenvects_square = sparse.linalg.eigsh(mean_ham**2, k=n_levels, which=\"LM\", sigma=np.min(potential)**2)\n",
|
|
"\n",
|
|
"tau = const.hbar/np.sqrt(np.abs(eigenvals_square - eigenvals**2))"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 91,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"tau_est = const.hbar/(np.max(energies,axis=0)-np.min(energies,axis=0))"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 92,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"[<matplotlib.lines.Line2D at 0x13da23c5be0>]"
|
|
]
|
|
},
|
|
"execution_count": 92,
|
|
"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,\"o\")\n",
|
|
"plt.plot(tau_est,\"o\")"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"### Do the same, but calculate average potential first"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 93,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
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"<Figure size 640x480 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"average_pot = sp.lambdify(y,trap.subs(-trap.a*np.sqrt(2/np.pi)/initial_distance*((trap.power_tweezer1/trap.waist_tweezer1*erf((initial_distance-2*y)/np.sqrt(2)/trap.waist_tweezer1)) +\n",
|
|
" (trap.power_tweezer2/trap.waist_tweezer2*erf((initial_distance+2*y)/np.sqrt(2)/trap.waist_tweezer2)))))\n",
|
|
"average_potential = average_pot(x_np)\n",
|
|
"plt.plot(x_np,average_potential)\n",
|
|
"\n",
|
|
"mean_ham2 = discrete_hamiltonian(dx,average_potential,float(trap.subs(trap.m).evalf()))\n",
|
|
"\n",
|
|
"\n",
|
|
"eigenvals2, eigenvects2 = sparse.linalg.eigsh(mean_ham2, k=n_levels, which=\"LM\", sigma=np.min(potential))\n",
|
|
"eigenvals2_square, eigenvects2_square = sparse.linalg.eigsh(mean_ham2**2, k=n_levels, which=\"LM\", sigma=np.min(potential)**2)\n",
|
|
"\n",
|
|
"tau2 = const.hbar/np.sqrt(np.abs(eigenvals2_square - eigenvals2**2))"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 94,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"[<matplotlib.lines.Line2D at 0x13da3741ee0>]"
|
|
]
|
|
},
|
|
"execution_count": 94,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
},
|
|
{
|
|
"data": {
|
|
"image/png": "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",
|
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"text/plain": [
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"<Figure size 640x480 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"#plt.plot(tau,\"o\")\n",
|
|
"plt.plot(tau2,\"o\")\n",
|
|
"plt.plot(tau_est,\"o\")\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Do it actually correctly (implemented in 1st section)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 95,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"ename": "IndexError",
|
|
"evalue": "index 10 is out of bounds for axis 1 with size 10",
|
|
"output_type": "error",
|
|
"traceback": [
|
|
"\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
|
|
"\u001b[1;31mIndexError\u001b[0m Traceback (most recent call last)",
|
|
"Cell \u001b[1;32mIn[95], line 14\u001b[0m\n\u001b[0;32m 12\u001b[0m delta_ham \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mzeros(n_levels)\n\u001b[0;32m 13\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m i, dist \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28menumerate\u001b[39m(distances):\n\u001b[1;32m---> 14\u001b[0m delta_ham[i] \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39msqrt(states[\u001b[38;5;241m-\u001b[39m\u001b[38;5;241m1\u001b[39m,i]\u001b[38;5;241m.\u001b[39mdot(mean_ham_square\u001b[38;5;241m.\u001b[39mdot(states[\u001b[38;5;241m-\u001b[39m\u001b[38;5;241m1\u001b[39m,i]))\u001b[38;5;241m-\u001b[39m(states[\u001b[38;5;241m-\u001b[39m\u001b[38;5;241m1\u001b[39m,i]\u001b[38;5;241m.\u001b[39mdot(mean_ham\u001b[38;5;241m.\u001b[39mdot(states[\u001b[38;5;241m-\u001b[39m\u001b[38;5;241m1\u001b[39m,i])))\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m2\u001b[39m)\n\u001b[0;32m 15\u001b[0m tau \u001b[38;5;241m=\u001b[39m const\u001b[38;5;241m.\u001b[39mhbar\u001b[38;5;241m/\u001b[39mdelta_ham\n",
|
|
"\u001b[1;31mIndexError\u001b[0m: index 10 is out of bounds for axis 1 with size 10"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"#calculate average potential as tweezer distance is decreased from \"initial_distance\" to zero\n",
|
|
"average_pot = sp.lambdify(y,trap.subs(-trap.a*np.sqrt(2/np.pi)/initial_distance*((trap.power_tweezer1/trap.waist_tweezer1*erf((initial_distance-2*y)/np.sqrt(2)/trap.waist_tweezer1)) +\n",
|
|
" (trap.power_tweezer2/trap.waist_tweezer2*erf((initial_distance+2*y)/np.sqrt(2)/trap.waist_tweezer2)))))\n",
|
|
"average_potential = average_pot(x_np)\n",
|
|
"#plt.plot(x_np,average_potential)\n",
|
|
"\n",
|
|
"#get the time averaged hamiltonian\n",
|
|
"mean_ham = discrete_hamiltonian(dx,average_potential,float(trap.subs(trap.m).evalf()))\n",
|
|
"mean_ham_square = mean_ham**2\n",
|
|
"\n",
|
|
"#compute the time \"tau\" needed to make it an adiabatic process\n",
|
|
"delta_ham = np.zeros(n_levels)\n",
|
|
"for i, dist in enumerate(distances):\n",
|
|
" delta_ham[i] = np.sqrt(states[-1,i].dot(mean_ham_square.dot(states[-1,i]))-(states[-1,i].dot(mean_ham.dot(states[-1,i])))**2)\n",
|
|
"tau = const.hbar/delta_ham"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Try to calculate phase imparted on the states"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 34,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"(150, 10)"
|
|
]
|
|
},
|
|
"execution_count": 34,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"energies.shape"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 35,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"(150, 10, 2000)"
|
|
]
|
|
},
|
|
"execution_count": 35,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"states.shape"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 36,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"#calculate dynamical phase\n",
|
|
"dyn_phase = -np.sum(energies,axis=0)/const.hbar\n",
|
|
"\n",
|
|
"#calculate geometric phase\n",
|
|
"dot_m = np.gradient(states,axis=0)\n",
|
|
"bracket_m_dot_m = np.sum(states*np.conjugate(dot_m),axis=2)\n",
|
|
"geo_phase = 1j*np.sum(bracket_m_dot_m,axis=0)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 37,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"array([-0.-0.69885833j, -0.-0.6988583j , -0.-0.94850139j, -0.-0.9485013j ,\n",
|
|
" -0.-0.02460082j, 0.+0.02460068j, -0.-0.04092669j, 0.+0.04092651j,\n",
|
|
" 0.+0.98219236j, -0.-0.98219215j])"
|
|
]
|
|
},
|
|
"execution_count": 37,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"geo_phase #this can't be correct, since it should be real!!!"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 38,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"array([47445210.80639105, 46774256.50928428, 44073351.11611445,\n",
|
|
" 43392945.91945135, 40776693.40224414, 40091176.83504527,\n",
|
|
" 37560433.80642757, 36872657.12805155, 34428490.8809985 ,\n",
|
|
" 33740893.13537717])"
|
|
]
|
|
},
|
|
"execution_count": 38,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"dyn_phase"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 39,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"ename": "ValueError",
|
|
"evalue": "operands could not be broadcast together with shapes (2,) (10,) ",
|
|
"output_type": "error",
|
|
"traceback": [
|
|
"\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
|
|
"\u001b[1;31mValueError\u001b[0m Traceback (most recent call last)",
|
|
"Cell \u001b[1;32mIn[39], line 1\u001b[0m\n\u001b[1;32m----> 1\u001b[0m c_new \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m1\u001b[39m\u001b[38;5;241m/\u001b[39mnp\u001b[38;5;241m.\u001b[39msqrt(\u001b[38;5;241m2\u001b[39m)\u001b[38;5;241m*\u001b[39mnp\u001b[38;5;241m.\u001b[39marray([\u001b[38;5;241m1\u001b[39m,\u001b[38;5;241m-\u001b[39m\u001b[38;5;241m1\u001b[39m])\u001b[38;5;241m*\u001b[39mnp\u001b[38;5;241m.\u001b[39mexp(\u001b[38;5;241m1\u001b[39mj\u001b[38;5;241m*\u001b[39m(geo_phase\u001b[38;5;241m+\u001b[39mdyn_phase))\n\u001b[0;32m 2\u001b[0m c_new\n",
|
|
"\u001b[1;31mValueError\u001b[0m: operands could not be broadcast together with shapes (2,) (10,) "
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"c_new = 1/np.sqrt(2)*np.array([1,-1])*np.exp(1j*(geo_phase+dyn_phase))\n",
|
|
"c_new"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": []
|
|
}
|
|
],
|
|
"metadata": {
|
|
"kernelspec": {
|
|
"display_name": "base",
|
|
"language": "python",
|
|
"name": "python3"
|
|
},
|
|
"language_info": {
|
|
"codemirror_mode": {
|
|
"name": "ipython",
|
|
"version": 3
|
|
},
|
|
"file_extension": ".py",
|
|
"mimetype": "text/x-python",
|
|
"name": "python",
|
|
"nbconvert_exporter": "python",
|
|
"pygments_lexer": "ipython3",
|
|
"version": "3.12.7"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 2
|
|
}
|