Reduction of frequency-dependent light shifts in light-narrowing regimes: A study using effective master equations

Abstract

Alkali-metal-vapor magnetometers, using coherent precession of polarized atomic spins for magnetic field measurement, have become one of the most sensitive magnetic field detectors. Their application areas range from practical uses such as detections of NMR signals to fundamental physics research such as searches for permanent electric dipole moments. One of the main noise sources of atomic magnetometers comes from the light shift that depends on the frequency of the pump laser. In this work, we theoretically study the light shift, taking into account the relaxation due to the optical pumping and the collision between alkali atoms and between alkali atoms and the buffer gas. Starting from a full master equation containing both the ground and excited states, we adiabatically eliminate the excited states and obtain an effective master equation in the ground-state subspace that shows an intuitive picture and dramatically accelerates the numerical simulation. Solving this effective master equation, we find that in the light-narrowing regime, where the line width is reduced while the coherent precession signal is enhanced, the frequency-dependence of the light shift is largely reduced, which agrees with experimental observations in cesium magnetometers. Since this effective master equation is general and is easily solved, it can be applied to an extensive parameter regime, and also to study other physical problems in alkali-metal-vapor magnetometers, such as heading errors.

Nuclear Zeeman Effect on Heading Errors and the Suppression in Atomic Magnetometers

“…With the experimental condition: in a magnetic shield, a 4 3 mm 3 85 Rb cell with 700Torr N 2 is heated to 90 Celsius, the pump laser's power is about 90 µW with the detuning ∆ = ∆ P , the probe laser propagating parallel to the driving field is about 0.2nm detuned from the D1 transition, we solve numerically the master equation ( 1) by adiabatically eliminating the excited states [27] and applying the linear response theory [28] for the RF driv-ing [22]. The difference between the measured precession frequency ω 0 (θ) and the Larmor frequency ω L is plotted in the lower part of Figs.…”

“…In the steady state ρ 0 , the population in the excited states are negligible because their decay rates is much larger than the Rabi frequency. Therefore, in the zero-order master equation ∂ t ρ = L 0 ρ, we can adiabatic eliminate the excited state and acquire an effective master equation in the ground-state subspace [22,27]. For this purpose, we rewrite the Lindblad operator L 0 as L 0 = L (0) 0 + L (1) 0 , where…”

“…Heading errors in atomic magnetometers have been studied both theoretically and experimentally [11,[14][15][16][17]. It has been shown [17] that the main contributions to the heading error are the nonlinear Zeeman (NLZ) effects [18,19] and the light shift (LS) [20][21][22] that is orientation dependent. In many of these studies, apart from a small correction to the Larmor frequency, the interaction between the external magnetic field and the nuclear spins is neglected since the nuclear magneton µ N is about 3 orders smaller than the Bohr magneton µ B .…”

Theory of light narrowing of magnetic resonances of alkali-metal atoms in the geophysical field range

“…This effect is caused by a reduction of SEC broadening due to optical pumping of most atoms into a stretched state (the state with the maximum or minimum magnetic quantum number m). A detailed explanation has been demonstrated in cesium atoms by investigating the orientation buildup in the ground state (uncoupled (off-resonance) to the pump beam) by indirect optical pumping combined with SEC [12,13], and this combined action simultaneously creates three performance: (a) removes population from F = 3 (being directly coupled (near-resonance) to the pump beam), (b) builds up orientation in the F = 4 manifold, thus increasing the signal amplitude on m = −4 ↔ m = −3 resonance, and (c) reduces the linewidth of that resonance. This type of light narrowing is beneficial for many precision measurements [14][15][16] even in a tilted magnetic field [17].…”

Quadrupole Effects on Nuclear Magnetic Resonance Gyroscopes

“…1) to reduce radiation trapping [8] and wall-collisions of the alkali atoms. A static magnetic filed B 0 along the z direction is applied in this atomic cell, and a circularly polarized laser is used to optically pump [9][10][11][12] the alkali atoms. Then the nobles gas are polarized via spin exchange [13][14][15][16][17] with the polarized alkali atoms, and in presence of a feedbackgenerated AC magnetic field along the x axis, the noblegas nuclear spins precess with a frequency that depends on the applied magnetic field and rotation of the system.…”