Atomic magnetometry^[1,2] has been extensively investigated in the past decades. The sensitivity of atomic magnetometry is related to the spin relaxation and it can be measured by observing the change of atomic polarization in a magnetic field.^[3] In this measurement, optical pumping is necessary to generate the atomic polarization^[4] through the absorption–emission cycle of atom–light interaction,^[5,6] and such optical pumping process has been considered as one of the fundamentals of magnetic field measurement.^[7,8] The atomic spin relaxation time T₂ in the vapor cell is a very important parameter which directly determines the sensitivity of an atomic magnetometer.^[9–11] The spin relaxation in the vapor cell is affected by many factors, such as diffusion of atoms,^[12,13] collision between atoms,^[14–16] optical pumping, etc. The relaxation caused by diffusion and collision can be suppressed by some advanced techniques, such as atom-relaxation coating of the vapor cell,^[17] optimizing the filling of buffer gas,^[18] controlling the temperature of the vapor cell,^[19] reducing the magnetic field gradient,^[20] etc. The relaxation caused by optical pumping can be controlled by optimizing the pump intensity,^[21] which is inevitable and cannot be eliminated completely.

The atomic spin relaxation time T₂ is characterized by the magnetic resonance linewidth (MRL) of the light-induced magnetic resonance Δ ω (Δ ω = 1/T₂).^[10,22] By observing the atomic polarization in different magnetic field around zero-point (so called zero-field resonance),^[23] or by tuning the modulation frequency of the pump beam around the magnetic resonance frequency,^[24–26] the magnetic resonance spectrum (MRS) can be measured. For a linear pump, the magnetic resonance frequency is equal to twice of the Larmor frequency (2 ω_L).^[27,28] The magnetic resonance process can be treated by Bloch equations and the MRS can be figured out which is normally a Lorentzian shape,^[29] from which the MRL (the half width at half maximum of MRS) is obtained.^[30]

Usually, the MRL can simply be treated as linear broadening^[22,31] with the increase of the pump intensity. However this treatment is actually incomplete. In 1999, the nonlinear light narrowing was investigated theoretically and experimentally,^[21] and the nonlinear broadening was also analyzed later^[32] based on a simplified ideal atomic system. By solving the Liouville equation with an unmodulated pump beam, the nonlinear broadening was obtained. Recently, Han et al. finished the experimental testing of pump induced nonlinear broadening in a heated rubidium vapor cell, in which the circularly polarized pump beam was amplitude modulated.^[33]

In this paper, we have investigated the influence of the pump intensity on spin relaxation at room temperature. The experiment is performed with a cesium vapor cell with buffer gas, and an unmodulated linear polarized pump beam locked to the D₁ line of cesium is used. The MRL is measured with the probe beam tuned on resonance to the D₂ transition. The MRL is measured at zero-field resonance, and the results show that the relation between MRL and pump intensity is nonlinear broadening. To the best of our knowledge, this is the first time this phenomenon is observed experimentally. We have also used a simplified five-level atomic system model with one excited state and four ground states to represent our experimental configuration, and by solving the Liouville equation,^[34,35] the experimental result can be explained approximately.

The experiment for testing the influence of the pump intensity on atomic spin relaxation is carried out at room temperature (∼ 25 °C), and the experimental setup is shown in Fig. 1. The system includes three parts: the vapor cell, the laser system, and the detection system.

Fig. 1.

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Fig. 1. Experimental setup for measuring the MRL. BS: beam splitter; PSL: the laser frequency control system by polarization spectrum locking technique; SAS, saturated absorption spectrum; HWP, half-wave plate; PBS, polarization beam splitter; HR, highly reflective mirror; GTP, Glan–Taylor prism; WP, Wollaston prism; BPD, balanced photodetector; AC, alternating current power supply; OSC, oscilloscope. The involved energy levels of cesium atom are shown in the upper right. mF and denote the magnetic quantum numbers of the ground and excited states, respectively. The Z polarized pump beam and the Y polarized probe beam are resonance to cesium D1 line 62S1/2 F = 4 to 62 P1/2 F′ = 3 and D2 line 62 S1/2 F = 4 to 62 P3/2 F′ = 5, respectively. The magnetic field (along the X direction) can be changed near the zero point by sweeping the driving current of the Helmholtz coil via AC, and the MRL can be obtained via OSC.

The vapor cell The cesium vapor cell has dimensions of 20 mm × 20 mm × 20 mm, and contains 20 Torr of helium as a buffer gas. The cell is put into a magnetic field along the X direction that is created by a pair of Helmholtz coils, which is driven by an alternating current power supply (AC, SRS DS335). The entire system is set in a magnetic shield cylinder, in which the residual magnetism is less than 2 nT.

The laser system The pump laser is polarized along the Z direction, and it is tuned to resonant to the cesium D₁ transition 6²S_1/2 F = 4 to 6²P_1/2 F′ = 3. The probe laser is polarized along the Y direction with a fixed intensity of 0.02 mW/cm², and the probe frequency is locked to the cesium D₂ line 6²S_1/2 F = 4 to 6²P_3/2 F′ = 5. Here, F and F′ represent the atomic total angular momenta of the ground and excited states, respectively.

The detection system The polarization of the probe beam transmitted through the vapor cell is detected by a balanced polarimeter, which is formed by a Wollaston prism (WP) and a balanced photodetector (BPD, New Focus 2307). The MRS of zero-field resonance for a fixed pump intensity can be measured by sweeping the magnetic field around the zero point (as shown in Fig. 2(a)), the MRS can be fitted by the dispersive Lorentzian shape, then the MRL can be obtained.

Fig. 2.

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Fig. 2. Experimental results for measuring the MRL. (a) MRS for a fixed pump intensity of 0.03 mW/cm2. The MRS is shown as the output of the balanced photodetector as a function of the magnetic resonance frequency 2 ωL = 2 γ B, where γ = 2π × 3.5 Hz/nT for the ground state of the cesium atom. The MRS is fitted by the dispersive Lorentzian shape (blue line, the red line is the experimental result), and the MRL is figured out as Δ ω = 2π × (93.5 ± 0.1) Hz (see the point with a black dotted cycle in (b)). (b) Relation between MRL and pump intensity. The red dots are the experimental results and the solid blue line is the theoretical fitting according to Eq. (12) (see the theoretical discussion below). Nonlinear relation is clearly shown and each data point and the error bar are obtained from five measurements. The best fitting gives the following parameters: α = 2π × (2.1 ± 0.2) × 103 Hz · cm2/mW and r0 = 2π × (69.7 ± 4.4) Hz.

The dependence of MRL on the pump intensity is shown in Fig. 2(b). The red dots are the experimental results. Nonlinear broadening is clearly shown in the entire pump range, which is indeed quite different from the usual simple linear explanation and treatment,^[22] as mentioned above. The blue line in Fig. 2(b) is the theoretical fitting according to Eq. (12) and it agrees with the experiment results in some extent. We are going to discuss it below.

In this part, we are trying to give an explanation to the above observed results. As shown in Fig. 1, if we consider the interaction between cesium D₁ transition and linearly polarized pump beam, there are totally 23 Zeeman sublevels involved, which are too complex to be solved. The process can actually be simplified to a five-level system as shown in Fig. 3. The reasons are list as follows.

Fig. 3.

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Fig. 3. Simplified five-level configuration. The Zeeman sublevels in ground state 62S1/2 F = 4 are represented by three states: |1⟩, |2⟩, and |3⟩, and state |4⟩ represents the other ground state 62S1/2 F = 3. A resonance pump light linearly polarized along the Z direction couples ground state 62 S1/2 F = 4 and the excited state 62P1/2 F′ = 3 (represented by |e⟩) with Rabi frequency ΩR. The total spontaneous decay rate of |e⟩ is Γ0 = 2 π × 4.5 × 106 Hz for cesium. The decay rates of |e⟩ to |1⟩ and |3⟩ are defined as η Γ0, while the rate from |e⟩ to |4⟩ is θ Γ0. The direction of the magnetic field is along the X direction.

(I) Since all the Zeeman sublevels in excited state 6²P_1/2 F′ = 3 are involved in the optical pumping process, and all these Zeeman sublevels have the same spontaneous decay rate Γ₀^[6] (for cesium, Γ₀ = 2π × 4.5 × 10⁶ Hz), we can treat all these seven sublevels as one state |e⟩.

(II) The Zeeman sublevels in ground state 6²S_1/2 F = 4 are separated into two parts: the first part is the Zeeman sublevels involved in the optical pumping process, corresponding to −3 ⩽ m_F ⩽ 3, and this part can be represented as state |2⟩. The second part is the rest of the Zeeman sublevels, corresponding to m_F = 4 and m_F = −4, which can be represented as states |1⟩ and |3⟩, respectively.

(III) The ground state 6²S_1/2 F = 3 is not involved in the optical pumping process, but some of the atoms still fall into this ground state through spontaneous emission process from the excited state 6²P_1/2 F = 3, so we can represent these Zeeman sublevels as one state |4⟩.

Since we have simplified our atomic level system, the spontaneous decay rate from excited state |e⟩ to each ground state |1⟩, |2⟩, and |3⟩ must be modified. We use η Γ₀ and θ Γ₀ to represent the recalculated spontaneous decay rates from |e⟩ to balanced states (|1⟩ and |3⟩) and state |4⟩, respectively. η and θ can be estimated by using the dipole matrix elements^[36]

As shown in Fig. 3, the resonance pump light with linear polarization along Z direction couples |2⟩ and |e⟩ with Rabi frequency Ω_R, and the magnetic field is along the X direction. We choose Z direction as the quantization axis, and the time evolution of the density matrix of the system is given by the Liouville equation^[34]

The second and third terms in Eq. (2) represent the depopulation ( ) and repopulation ( ) of the ground and excited states without the influence of pump light and magnetic field, respectively. It should be mentioned that in the absence of the pump beam, the relaxation rates of the Zeeman sublevels are different due to spin exchange collisions.^[37] In our model, for the sake of simplicity, we consider the same relaxation rate, represented as r₀. Under this condition, depopulation and repopulation should be

A probe beam is used to detect the component of the atomic polarization in 6²S_1/2 F = 4 along the Y direction, which can be expressed by an operator . From the symmetry shown in relation (6), can be considered as a combination of the atomic polarizations in state 6²S_1/2 F = 4 along the positive Y direction ( ) and negative Y direction ( )^[38]

The dependence of on the parameter u with certain pump intensity has a dispersive Lorentzian shape, and its half width at half maximum Δ u is directly proportional to the MRL Δ ω = Δ u × r₀. Thus, Δ ω can be expressed as

We have investigated the influence of the pump intensity on atomic spin relaxation. The spin relaxation is characterized by the MRL. The experiment is performed in a cesium vapor cell with 20 Torr helium as a buffer gas at room temperature. The nonlinear broadening of MRL along with the pump intensity increasing is observed. A simplified five-level atomic configuration is analyzed which can represent our experiment system to a certain extent, and the dependence of the MRL on pump intensity is obtained theoretically. The nonlinear relation between MRL and pump intensity is expected, which explains our experimental results to some extent. The reported results provide a better understanding of the atom–field interaction in atomic magnetometers.