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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 19 — Sep. 14, 2009
  • pp: 16776–16782
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Atomic magnetometry with maximally polarized states

Ran Fischer, Ofer Firstenberg, Moshe Shuker, and Amiram Ron  »View Author Affiliations


Optics Express, Vol. 17, Issue 19, pp. 16776-16782 (2009)
http://dx.doi.org/10.1364/OE.17.016776


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Abstract

A new magnetometry method based on electromagnetic induced transparency (EIT) with maximally polarized states is demonstrated. An EIT hyperfine resonance, comprising the mF=F state (end-state), is observed at a non-zero angle between the laser beam and the magnetic field. The method takes advantage of the process of end-state pumping, a well-known rival of simpler EIT magnetometry schemes, and therefore benefits at a high laser power. An experimental demonstration and a numerical analysis of the magnetometry method are presented. The analysis points on a clear sensitivity advantage of the end-state EIT magnetometer.

© 2009 OSA

1. Introduction

In an optical magnetometer, the Larmor frequency or the Zeeman splitting, due to the presence of a magnetic field, is measured through the interaction of light and atoms [‎1]. The field of optical magnetometry is roughly divided into two detection techniques: non-linear magneto-optical rotation [‎2], based on measuring the polarization rotation of a probe laser [‎3, ‎4, ‎5], and intensity detection, which utilizes a narrow and steep change in the probe transmission due to electromagnetically induced transparency (EIT) [‎6, ‎7, ‎8]. In the latter, a sample of alkali atoms is probed by two laser beams or electromagnetic modes, with a frequency difference that corresponds to the splitting of two magnetic-sensitive levels [‎9]. At Raman resonance conditions, the atoms reach a coherent superposition in which the absorption decreases significantly. The magnetic field determines the frequency of the resonance, and the accuracy of the method is determined by the width and amplitude of the resonance.

In a simple magnetometry configuration, an EIT transition is created with a circularly polarized light between two hyperfine ground-state sub-levels with the same mF0, where mF is the projection of angular momentum in the direction of the magnetic field. Figure 1a
Fig. 1 (a) Level scheme of the D1 transition in 87Rb. The blue arrows represent the (0,0) resonance (the so-called clock resonance), the dashed arrows represent the ( + 1, + 1) resonance, and the red arrows represent the ( + 1, + 2) resonance. (b) The experimental system (see description in text).
depicts this transition with mF=1, for the D1 manifold of 87Rb (dashed lines). The resonance frequency depends on the Zeeman shifts of the lower states involved. Two major trade-offs limit the performance of this scheme. First, increasing the laser power in order to improve the coherent pumping into the EIT state results in a power broadening of the resonance and also incoherently pumps the atoms away from the EIT system and towards the maximally polarized states (end states). Second, increasing the density in order to increase the line's amplitude results in an elevated spin-exchange decoherence rate, broadening the resonance. These factors impose an upper limit on both the laser power and the atomic density. Here, we introduce a new EIT magnetometry method which overcomes these disadvantages. The method exploits the beneficial characteristics of an EIT resonance with the maximally polarized states; it is enhanced due to both coherent and incoherent pumping, and it is substantially more resistant to spin-exchange [‎10].

In many cases, spin-exchange collisions are the dominant decoherence mechanism in the system and the primary limitation to the magnetometer sensitivity. Around 50°C (atomic density of ~1011 cm−3), for example, spin exchange determines the width of the resonance to the order of 100 Hz, compared with the Zeeman splitting, of the order of 107 KHz/Tesla. In the current work, we perform the experiments at a low Rubidium density, in which spin-exchange relaxation is negligible relatively to the other decoherence mechanisms. Therefore, we do not examine the improved spin-exchange resistance and concentrate on the analysis of the pumping mechanism. In section 2, we introduce the principles of the suggested magnetometry method, alongside an analysis of its advantages. In section 3, we describe the experimental system and the main results achieved. The last section includes an in-depth comparison of the two EIT-based magnetometry methods, through detailed numerical simulations, which accurately reproduce the experimental results.

2. Principle of operation

We study the suggested magnetometry method within the D1 transition of 87Rb. The energy-levels scheme is depicted in Fig. 1a, showing various possible EIT ground-state resonances. Specifically, we study the EIT resonance ( + 1, + 2), involving the two ground-state sub-levels |F=1,mF=+1 and |F=2,mF=+2 (solid and dashed red arrows in the figure), and compare it to the EIT resonance ( + 1, + 1), involving the |F=1,mF=+1and |F=2,mF=+1 (red and green dashed arrows). The end-state resonance can be observed when the propagation direction of a right-circularly polarized beam (σ+) is at a non-zero angle θ to the magnetic field direction, which defines the quantization axis. In that case, the electric field of the laser can be expressed in the form of all possible polarizations [‎7],

E=E(isinθ2π^+1+cosθ2σ++1+cosθ2σ),
(1)

where,

σ^+=x^iy^2       ;       σ^=x^+iy^2     ;     π^=iz^.
(2)

The ratio of the different polarizations, and thus the intensities of different EIT resonances, is controlled by the angle between the beam and the magnetic field (see Fig. 1b). In a practical system, this magnetometer can exploit the advantages of the optimal-performance angle by tuning to this angle, either by a physical alignment of the system or by applying a DC magnetic field in the optimal direction.

We identify three distinct advantages of the ( + 1, + 2) magnetometer over the ( + 1, + 1) magnetometer. First, the Zeeman splitting of the ( + 1, + 2) resonance is 1.5 times that of the ( + 1, + 1) resonance. Second, for θ<90°, the σ+ light intensity exceeds the σ intensity, resulting in an incoherent pumping of the alkali population towards the end state. This pumping increases the contrast of the ( + 1, + 2) resonance, which comprises the high mF states of the ground manifold, but decreases the contrast of all other resonances [‎11]. Third, when most of the atomic population is pumped to the end state, the spin-exchange decoherence rate is reduced, narrowing the EIT resonance. The latter is especially pronounced in miniature cells due to the high atomic density required.

In the following sections, we compare the experimental results with an elaborated numerical model. Our numerical model takes into account all 16 sub-levels of the D1 transition and the three laser polarizations. The system is modeled by means of solving the Master's equation,

ddtρ=ih[H,ρ]+Lρ,
(3)

where ρ is the density matrix of the Rubidium atom, H=H0+HC is the full Hamiltonian of the system. Here H0 is the free Hamiltonian, HCis the interaction Hamiltonian, and L is the Lindblad super-operator which effectively describes the decay and decoherence processes at the ground and the excited states of the Rubidium atoms. In HC, we take into account all the allowed transitions, with their respective dipole amplitudes (Clebsch-Gordan coefficients), including those that are far detuned from resonance (12 transitions for each polarization component). The ground-state decoherence rate (γ12) and the laser power (in terms of the power broadening ΓP), were calibrated from the θ=0 measurement, depicted in Fig. 2
Fig. 2 Frequency scan of the RF modulation in 6 experiments (full lines) and the corresponding simulations (dashed lines). f0 is the frequency of the clock transition. The EIT lines, from left to right, are the (0,0) clock line, (0, + 1) line, ( + 1, + 1) line, and ( + 1, + 2) line. The angle between the magnetic field and beam is 0 (blue), 5, 15, 25, 34 and 40 (brown) degrees. Inset: The ratio between the frequency of the EIT lines and ωZeeman(+1,+1).
(blue), to be approximately γ12=500Hzand ΓP=1.5KHz. A more elaborated description of the numerical model is given in ref. [‎12].

3. Experimental setup & results

The experimental system is depicted in Fig. 1b. A Vertical Cavity Surface Emitting Laser (VCSEL) is tuned to the D1 transition of 87Rb (~795nm). The VCSEL is current-modulated at fRF3.4  GHz, creating two main sidebands with f=2×fRF6.8  GHz, matching the hyperfine splitting of the 87Rb ground-state and carrying an intensity of approximately 0.1 mW/cm2 each. The light that enters the vapor cell is σ+ polarized by a linear polarizer and a quarter wave plate. The vapor cell is placed in a 4-layer magnetic shield, which attenuates the Earth magnetic field. Three pairs of Helmholtz coils located inside the shield, enable us to control the magnitude and the direction of the magnetic field. The vapor cell is about 25 mm long and contains isotopically pure 87Rb with 10 torr of Nitrogen buffer gas. The experiments were conducted at temperatures of 40-50 °C providing a vapor density of ~5⋅1010 cm−3.

4. Discussion

In a typical magnetometer set-up, the magnetic field is deduced from a measurement of the magnetic resonance frequency. The possible accuracy is governed by two factors: the magnetic field sensitivity of the shift in the central frequency and the width and amplitude of the resonance. The magnetic field dependence of the central frequency (δf) is determined by the relative Zeeman splitting. For 87Rb ground-state, the frequency dependence is 1.4 KHz/mG for the ( + 1, + 1) resonance and 2.1 KHz/mG for the ( + 1, + 2) resonance.

In order to compare the relative accuracy of the suggested magnetometer scheme to the ( + 1, + 1) scheme, we define a figure of merit (FOM), given by

FOM=δf[KHz/mG]ContrastFWHM[KHz].
(4)

FOM=δf[d(Imχ)dΔ]|Δ=0.
(5)

In conclusion, we have introduced an EIT magnetometry method that exploits the advantages of maximally-polarized states. The measurements and the simulations exhibit some of these advantages over the simple ( + 1, + 1) magnetometry. We have concentrated mainly on the role of the pumping mechanism in determining the sensitivity of the schemes. Two possible contributions to the sensitivity of the method were not analyzed here - decrease in the spin-exchange relaxation, which is especially relevant at miniature systems, and improvement in the signal-to-noise ratio. The behavior of the new scheme in a high-density regime dominated by spin-exchange relaxation and the noise properties of the method is left for future research.

Acknowledgements

We acknowledge helpful discussions with Amnon Fisher and Paz London. We thank Yoav Erlich for technical support. This work is partially supported by the fund for encouragement of research in the Technion and by the DDRND.

References and links

1.

D. Budker and M. Romalis, “Optical magnetometry,” Nat. Phys. 3(4), 227–234 (2007), http://dx.doi.org/10.1038/nphys566. [CrossRef]

2.

D. Budker, W. Gawlik, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and A. Weis, “Resonant nonlinear magneto-optical effects in atoms,” Rev. Mod. Phys. 74(4), 1153–1201 (2002), http://link.aps.org/doi/10.1103/RevModPhys.74.1153. [CrossRef]

3.

D. Budker, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and M. Zolotorev, “Sensitive magnetometry based on nonlinear magneto-optical rotation,” Phys. Rev. A 62(4), 043403 (2000), http://link.aps.org/doi/10.1103/PhysRevA.62.043403. [CrossRef]

4.

I. K. Kominis, T. W. Kornack, J. C. Allred, and M. V. Romalis, “A subfemtotesla multichannel atomic magnetometer,” Nature 422(6932), 596–599 (2003), http://dx.doi.org/10.1038/nature01484. [CrossRef] [PubMed]

5.

P. D. D. Schwindt, L. Hollberg, and J. Kitching, “Self-oscillating rubidium magnetometer using nonlinear magneto-optical rotation,” Rev. Sci. Inst. 76(12), 126103 (pages 4) (2005). http://link.aip.org/link/?RSINAK/76/126103/1.

6.

P. D. D. Schwindt, S. Knappe, V. Shah, L. Hollberg, and J. Kitching, “Chip-scale atomic magnetometer,” App. Phys. Lett. 85(26), 6409–6411 (2004). http://link.aip.org/link/?APL/85/6409/1.

7.

H. Lee, M. Fleischhauer, and M. O. Scully, “Sensitive detection of magnetic fields including their orientation with a magnetometer based on atomic phase coherence,” Phys. Rev. A 58(3), 2587–2595 (1998), http://link.aps.org/doi/10.1103/PhysRevA.58.2587. [CrossRef]

8.

J. Belfi, G. Bevilacqua, V. Biancalana, S. Cartaleva, Y. Dancheva, and L. Moi, “Cesium coherent population trapping magnetometer for cardiosignal detection in an unshielded environment,” J. Opt. Soc. Am. B 24(9), 2357–2362 (2007), http://josab.osa.org/abstract.cfm?URI=josab-24-9-2357. [CrossRef]

9.

E. Arimondo, Coherent Population Trapping in Laser Spectroscopy, Progress in Optics, vol. 35 (Elsevier, Amsterdam, 1996).

10.

Y.-Y. Jau, A. B. Post, N. N. Kuzma, A. M. Braun, M. V. Romalis, and W. Happer, “Intense, narrow atomic-clock resonances,” Phys. Rev. Lett. 92(11), 110801 (2004), http://link.aps.org/doi/10.1103/PhysRevLett.92.110801. [CrossRef] [PubMed]

11.

J. Vanier, M. W. Levine, D. Janssen, and M. Delaney, “Contrast and linewidth of the coherent population trapping transmission hyperfine resonance line in 87Rb: Effect of optical pumping,” Phys. Rev. A 67(6), 065801 (pages 4) (2003). http://link.aps.org/doi/10.1103/PhysRevA.67.065801.

12.

M. Shuker, O. Firstenberg, Y. Sagi, A. Ben-kish, N. Davidson, and A. Ron, “Ramsey-like measurement of the decoherence rate between Zeeman sublevels,” Phys. Rev. A 78(6), 063818 (pages 7) (2008). http://link.aps.org/abstract/PRA/v78/e063818.

OCIS Codes
(020.3690) Atomic and molecular physics : Line shapes and shifts
(270.1670) Quantum optics : Coherent optical effects

ToC Category:
Quantum Optics

History
Original Manuscript: June 1, 2009
Revised Manuscript: June 28, 2009
Manuscript Accepted: June 30, 2009
Published: September 4, 2009

Citation
Ran Fischer, Ofer Firstenberg, Moshe Shuker, and Amiram Ron, "Atomic magnetometry with maximally polarized states," Opt. Express 17, 16776-16782 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-19-16776


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References

  1. D. Budker and M. Romalis, “Optical magnetometry,” Nat. Phys. 3(4), 227–234 (2007), http://dx.doi.org/10.1038/nphys566 . [CrossRef]
  2. D. Budker, W. Gawlik, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and A. Weis, “Resonant nonlinear magneto-optical effects in atoms,” Rev. Mod. Phys. 74(4), 1153–1201 (2002), http://link.aps.org/doi/10.1103/RevModPhys.74.1153 . [CrossRef]
  3. D. Budker, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and M. Zolotorev, “Sensitive magnetometry based on nonlinear magneto-optical rotation,” Phys. Rev. A 62(4), 043403 (2000), http://link.aps.org/doi/10.1103/PhysRevA.62.043403 . [CrossRef]
  4. I. K. Kominis, T. W. Kornack, J. C. Allred, and M. V. Romalis, “A subfemtotesla multichannel atomic magnetometer,” Nature 422(6932), 596–599 (2003), http://dx.doi.org/10.1038/nature01484 . [CrossRef] [PubMed]
  5. P. D. D. Schwindt, L. Hollberg, and J. Kitching, “Self-oscillating rubidium magnetometer using nonlinear magneto-optical rotation,” Rev. Sci. Inst. 76(12), 126103 (pages 4) (2005). http://link.aip.org/link/?RSINAK/76/126103/1 .
  6. P. D. D. Schwindt, S. Knappe, V. Shah, L. Hollberg, and J. Kitching, “Chip-scale atomic magnetometer,” App. Phys. Lett. 85(26), 6409–6411 (2004). http://link.aip.org/link/?APL/85/6409/1 .
  7. H. Lee, M. Fleischhauer, and M. O. Scully, “Sensitive detection of magnetic fields including their orientation with a magnetometer based on atomic phase coherence,” Phys. Rev. A 58(3), 2587–2595 (1998), http://link.aps.org/doi/10.1103/PhysRevA.58.2587 . [CrossRef]
  8. J. Belfi, G. Bevilacqua, V. Biancalana, S. Cartaleva, Y. Dancheva, and L. Moi, “Cesium coherent population trapping magnetometer for cardiosignal detection in an unshielded environment,” J. Opt. Soc. Am. B 24(9), 2357–2362 (2007), http://josab.osa.org/abstract.cfm?URI=josab-24-9-2357 . [CrossRef]
  9. E. Arimondo, Coherent Population Trapping in Laser Spectroscopy, Progress in Optics, vol. 35 (Elsevier, Amsterdam, 1996).
  10. Y.-Y. Jau, A. B. Post, N. N. Kuzma, A. M. Braun, M. V. Romalis, and W. Happer, “Intense, narrow atomic-clock resonances,” Phys. Rev. Lett. 92(11), 110801 (2004), http://link.aps.org/doi/10.1103/PhysRevLett.92.110801 . [CrossRef] [PubMed]
  11. J. Vanier, M. W. Levine, D. Janssen, and M. Delaney, “Contrast and linewidth of the coherent population trapping transmission hyperfine resonance line in 87Rb: Effect of optical pumping,” Phys. Rev. A 67(6), 065801 (pages 4) (2003). http://link.aps.org/doi/10.1103/PhysRevA.67.065801 .
  12. M. Shuker, O. Firstenberg, Y. Sagi, A. Ben-kish, N. Davidson, and A. Ron, “Ramsey-like measurement of the decoherence rate between Zeeman sublevels,” Phys. Rev. A 78(6), 063818 (pages 7) (2008). http://link.aps.org/abstract/PRA/v78/e063818 .

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