"""
Physical Constants for AMO Physics
Comprehensive collection of physical constants, atomic data, and unit conversions.
"""
import numpy as np
from scipy import constants as const
from typing import Dict, Any, Optional
class FundamentalConstants:
"""Fundamental physical constants in SI units."""
# Speed of light
c = const.c # m/s
# Planck constants
h = const.h # J⋅s
hbar = const.hbar # J⋅s
# Electromagnetic constants
e = const.e # C (elementary charge)
epsilon_0 = const.epsilon_0 # F/m (vacuum permittivity)
mu_0 = const.mu_0 # H/m (vacuum permeability)
# Particle masses
m_e = const.m_e # kg (electron mass)
m_p = const.m_p # kg (proton mass)
m_n = const.m_n # kg (neutron mass)
u = const.u # kg (atomic mass unit)
# Boltzmann constant
k_B = const.k # J/K
# Fine structure constant
alpha = const.alpha # dimensionless
# Avogadro's number
N_A = const.N_A # mol⁻¹
class AtomicUnits:
"""Atomic units (Hartree system)."""
# Length
a0 = const.physical_constants['Bohr radius'][0] # m
# Energy
Eh = const.physical_constants['Hartree energy'][0] # J
Eh_eV = const.physical_constants['Hartree energy in eV'][0] # eV
# Electric field
E_h = const.e / (4 * np.pi * const.epsilon_0 * const.a_0**2) # V/m
# Time
t_au = const.hbar / AtomicUnits.Eh # s
# Velocity
v_au = const.alpha * const.c # m/s
class AtomicData:
"""Atomic data for common elements used in AMO physics."""
# Atomic masses (in atomic mass units)
masses = {
'H': 1.007825032,
'D': 2.014101778,
'T': 3.016049268,
'He': 4.002603254,
'Li': 6.015122887,
'Be': 9.012182201,
'B': 10.012936862,
'C': 12.000000000,
'N': 14.003074004,
'O': 15.994914620,
'F': 18.998403163,
'Ne': 19.992440175,
'Na': 22.989769282,
'Mg': 23.985041697,
'Al': 26.981538627,
'Si': 27.976926533,
'P': 30.973761998,
'S': 31.972071174,
'Cl': 34.968852682,
'Ar': 39.962383123,
'K': 38.963706679,
'Ca': 39.962590863,
'Rb': 86.909180527,
'Sr': 87.905614306,
'Cs': 132.905451931,
'Ba': 137.905247237,
'Yb': 173.938862089,
}
# Ionization potentials (in eV)
ionization_potentials = {
'H': 13.59844,
'He': 24.58741,
'Li': 5.39172,
'Be': 9.32270,
'B': 8.29803,
'C': 11.26030,
'N': 14.53414,
'O': 13.61806,
'F': 17.42282,
'Ne': 21.56454,
'Na': 5.13908,
'Mg': 7.64624,
'Al': 5.98577,
'Si': 8.15169,
'P': 10.48669,
'S': 10.36001,
'Cl': 12.96764,
'Ar': 15.75962,
'K': 4.34066,
'Ca': 6.11316,
'Rb': 4.17713,
'Sr': 5.69484,
'Cs': 3.89390,
'Ba': 5.21170,
'Yb': 6.25416,
}
# Common D-line transitions (wavelength in nm)
d_lines = {
'Li': {'D1': 670.776, 'D2': 670.791},
'Na': {'D1': 589.756, 'D2': 588.995},
'K': {'D1': 770.108, 'D2': 766.490},
'Rb': {'D1': 794.979, 'D2': 780.241},
'Cs': {'D1': 894.593, 'D2': 852.347},
}
# Natural linewidths (in MHz)
natural_linewidths = {
'Li_D1': 5.872,
'Li_D2': 5.872,
'Na_D1': 9.795,
'Na_D2': 9.795,
'K_D1': 6.035,
'K_D2': 6.035,
'Rb_D1': 5.746,
'Rb_D2': 6.066,
'Cs_D1': 4.560,
'Cs_D2': 5.234,
}
# Nuclear spins
nuclear_spins = {
'H': 1/2,
'Li': 3/2,
'Na': 3/2,
'K': 3/2,
'Rb': 3/2,
'Cs': 7/2,
'Sr': 0,
'Yb': 0,
}
class LaserParameters:
"""Common laser parameters and wavelengths."""
# Common laser wavelengths (in nm)
wavelengths = {
'HeNe_red': 632.8,
'HeNe_green': 543.5,
'Ar_blue': 488.0,
'Ar_green': 514.5,
'Ti_sapphire_center': 800.0,
'Nd_YAG_fundamental': 1064.0,
'Nd_YAG_second_harmonic': 532.0,
'Nd_YAG_third_harmonic': 355.0,
'Nd_YAG_fourth_harmonic': 266.0,
'CO2': 10600.0,
'diode_780': 780.0,
'diode_852': 852.0,
'diode_895': 895.0,
}
# Laser linewidths (typical values in Hz)
linewidths = {
'HeNe': 1e6, # ~1 MHz
'diode_free': 1e6, # ~1 MHz
'diode_stabilized': 1e3, # ~1 kHz
'Ti_sapphire': 1e5, # ~100 kHz
'external_cavity': 1e3, # ~1 kHz
'stabilized_cavity': 1, # ~1 Hz
}
class MagneticFields:
"""Magnetic field related constants."""
# Bohr magneton
mu_B = const.physical_constants['Bohr magneton'][0] # J/T
mu_B_eV_T = const.physical_constants['Bohr magneton in eV/T'][0] # eV/T
# Nuclear magneton
mu_N = const.physical_constants['nuclear magneton'][0] # J/T
mu_N_eV_T = const.physical_constants['nuclear magneton in eV/T'][0] # eV/T
# Landé g-factors (typical values)
g_factors = {
'electron': 2.002319304,
'proton': 5.585694702,
'neutron': -3.826085455,
}
# Earth's magnetic field (typical values in Tesla)
earth_field = {
'horizontal': 2e-5, # ~20 μT
'vertical': 4e-5, # ~40 μT
'total': 5e-5, # ~50 μT
}
class TrapParameters:
"""Parameters for common atomic traps."""
# Typical trap depths (in μK)
trap_depths = {
'magneto_optical': 1000, # 1 mK
'magnetic': 100, # 100 μK
'optical_dipole': 10, # 10 μK
'optical_lattice': 100, # 100 μK
}
# Typical trap frequencies (in Hz)
trap_frequencies = {
'magnetic_quadrupole': 100, # 100 Hz
'optical_dipole_tight': 1000, # 1 kHz
'optical_dipole_loose': 10, # 10 Hz
'optical_lattice': 10000, # 10 kHz
}
class ConversionFactors:
"""Unit conversion factors."""
# Energy conversions
J_to_eV = 1 / const.e
eV_to_J = const.e
K_to_eV = const.k / const.e # Boltzmann constant in eV/K
eV_to_K = const.e / const.k
Hz_to_eV = const.h / const.e
eV_to_Hz = const.e / const.h
# Length conversions
m_to_nm = 1e9
nm_to_m = 1e-9
m_to_a0 = 1 / AtomicUnits.a0
a0_to_m = AtomicUnits.a0
# Time conversions
s_to_ns = 1e9
ns_to_s = 1e-9
s_to_fs = 1e15
fs_to_s = 1e-15
# Frequency conversions
Hz_to_rad_s = 2 * np.pi
rad_s_to_Hz = 1 / (2 * np.pi)
# Temperature conversions
K_to_mK = 1e3
mK_to_K = 1e-3
K_to_uK = 1e6
uK_to_K = 1e-6
K_to_nK = 1e9
nK_to_K = 1e-9
def get_atomic_property(element: str, property_name: str) -> Optional[float]:
"""
Get atomic property for a given element.
Args:
element: Element symbol (e.g., 'Rb', 'Cs')
property_name: Property name ('mass', 'ionization_potential', etc.)
Returns:
Property value or None if not found
"""
if property_name == 'mass':
return AtomicData.masses.get(element)
elif property_name == 'ionization_potential':
return AtomicData.ionization_potentials.get(element)
elif property_name == 'nuclear_spin':
return AtomicData.nuclear_spins.get(element)
else:
return None
def calculate_recoil_energy(wavelength_nm: float, mass_amu: float) -> float:
"""
Calculate photon recoil energy.
Args:
wavelength_nm: Photon wavelength (nm)
mass_amu: Atomic mass (amu)
Returns:
Recoil energy (J)
"""
wavelength_m = wavelength_nm * 1e-9
mass_kg = mass_amu * const.u
momentum = const.h / wavelength_m
recoil_energy = momentum**2 / (2 * mass_kg)
return recoil_energy
def calculate_doppler_width(frequency_hz: float, temperature_k: float, mass_amu: float) -> float:
"""
Calculate Doppler broadening width.
Args:
frequency_hz: Transition frequency (Hz)
temperature_k: Temperature (K)
mass_amu: Atomic mass (amu)
Returns:
Doppler width (FWHM) in Hz
"""
mass_kg = mass_amu * const.u
# Most probable velocity
v_mp = np.sqrt(2 * const.k * temperature_k / mass_kg)
# Doppler width (FWHM)
doppler_width = 2 * frequency_hz * v_mp / const.c * np.sqrt(np.log(2))
return doppler_width
def wavelength_to_energy(wavelength_nm: float) -> float:
"""Convert wavelength to photon energy (eV)."""
wavelength_m = wavelength_nm * 1e-9
energy_j = const.h * const.c / wavelength_m
return energy_j / const.e # Convert to eV
def energy_to_wavelength(energy_ev: float) -> float:
"""Convert photon energy to wavelength (nm)."""
energy_j = energy_ev * const.e
wavelength_m = const.h * const.c / energy_j
return wavelength_m * 1e9 # Convert to nm
