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Physical Review Letters

Resonant Transfer of Coherence in Nonzero Magnetic Field Between Atomic Levels of Different g Factors

S. Haroche, Claude N. Cohen-Tannoudji

Published May 4, 1970• 48 citations
Publisher

Abstract

Coherence transfer between atomic levels requires the matching of the Larmor frequencies. For levels with different $g$ factors this occurs only in zero magnetic field. By changing the $g$ factors through coupling with a nonresonant rf field, one can match the Larmor frequencies and make the transfer possible in nonzero magnetic fields. Resonances in the transfer appear, depending on the rf field amplitude. ${\mathrm{Rb}}^{87}$-${\mathrm{Cs}}^{133}$ spin-exchange experiments are reported which provide an illustration of the theory.

DOI
10.1103/physrevlett.24.974

Related papers

Transfer of Precessing Spin Polarizations between Different Kinds of Atoms with Sameg-Factor

Taro Ito, Noboru Shimomura, T. Yabuzaki

In spin-related fundamental researches, there have been considerable interests in the transfer of microscopic orders between magnetic sublevels of different kinds of atoms. As for gaseous atomic systems, collisional transfer of spin polarization from optically pumped atoms A to atoms B is attained through spin exchange collisions. So far many experiments have been reported on the transfer of longitudinal spin polarization created along a static magnetic field. Transfer of coherence, on the other hand,is possible only when the energy matching condition j!A !Bj < is satisfied, where !A and !B are the Larmor frequencies of atoms A and B, and the line width. This is the reason why transfer of spin polarization precessing around the static magnetic field has not been observed except for a few experiments; The coherence transfer has been observed in the experiments where the atoms are subjected to properly chosen rf magnetic fields. Recently, it has been reported that coherence transfer between different kinds of atoms is possible by using the light field which transversely pumps only one kind of atoms under properly chosen experimetal conditions. It has also been pointed out that, as for the system of Rb and K atoms, which happen to have the same gyro-magnetic ratio, the peculier distortion of the magnetic resonance signal line shapes observed in the collisionally pumped atoms can be explained by the spin exchange coupling between the resonant Rb and K atoms. It is suggested that the precessing spin polarization in Rb can be transferred to K atoms or vice versa, since their Zeeman splittings become equal in the hyperfine multiplets jF 1⁄4 1i and jF 1⁄4 2i of the ground state 2S1=2 with the same gyromagnetic ratio 1⁄4 2 700 kHz/G. The experimental apparatus of the present experiment is shematically shown in Fig. 1. In addition to a droplet of natural rubidium and potassium, the sample cell contains 50mbar Ar as a buffer gas. It is subjected to a static magnetic field of H0 1⁄4 0:786G along the z axis and irradiated transversely to the field by a light beam from a GaAlAs laser A (output power = 10mW, beam diameter = 1mm). It is left-handed circularly polarized and tuned to the Rb absorption lines (S1=2, F 1⁄4 1 ! P1=2, F 1⁄4 1 and 2) which are not resolved owing to the Doppler broadening. The intensity of the laser A is modulated by an AOM (acousto-optic-modulator) at the Larmor frequency !A 1⁄4 2 550 (1⁄4 700 0:786) kHz of Rb in a rectangular shape pulse. As mentioned above the precessing spin polarization in Rb can be transferred to K. The precessing spin polarization of Rb and that of K are detected from the Faraday rotations of the beams of probe lasers B ( 1⁄4 794 nm, output power = 3mW, beam diameter = 2mm) and C ( 1⁄4 769 nm, output power = 3mW, beam diameter = 2mm), respectively. The frequency of laser B is chosen to be a few GHz higher than the Rb absorption lines (S1=2, F 1⁄4 1 ! P1=2, F 1⁄4 1 and 2) to prevent the detection beam from destroying the polarization. Similarly, the frequency of laser C is chosen to be a few GHz higher than the K absorption lines (S1=2, F 1⁄4 1 and 2 ! P1=2, F 1⁄4 1 and 2) which are not resolved owing to the Doppler broadening. They are linearly polarized and counter-propagated against the pumping beam,making angles of about 1 to the pumping beam. In each case the transmitted light beam of probe laser passes through the analyzer which makes an angle 45 to the polarization of the incident beam,and then it is detected by a pin-photo diode. The signals are electronically averaged over a few hundred cycles. Figure 2(a) shows the typical examples of signals on the magnetizations M x and M B x of Rb and K, respectively, Fig. 1. Schematic diagram of the experimetal apparatus. AOM, acoustooptic modulator; PD, pin-photo diode; P, polarizer; A, analyzer.

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Radio-frequency-driven dipole-dipole interactions in spatially separated volumes

Atreju Tauschinsky, C. S. E. van Ditzhuijzen, Lambertus D. Noordam +1 more

Radio-frequency (rf) fields in the MHz range are used to induce resonant energy transfer between cold Rydberg atoms in spatially separated volumes. After laser preparation of the Rydberg atoms, dipole-dipole coupling excites the $49s$ atoms in one cylinder to the $49p$ state while the $41d$ atoms in the second cylinder are transferred down to the $42p$ state. The energy exchanged between the atoms in this process is $33\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}$. An external rf field brings this energy transfer into resonance. The strength of the interaction has been investigated as a function of amplitude $(0--1\phantom{\rule{0.3em}{0ex}}\mathrm{V}∕\mathrm{cm})$ and frequency $(1--30\phantom{\rule{0.3em}{0ex}}\mathrm{MHz})$ of the rf field and as a function of a static-field offset. Multiphoton transitions up to fifth order as well as selection rules prohibiting the process at certain fields have been observed. The width of the resonances has been reduced compared to earlier results by switching off external magnetic fields of the magneto-optical trap, making sub-MHz spectroscopy possible. All features are well reproduced by theoretical calculations taking the strong ac Stark shift due to the rf field into account.

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Effect of rapid spin exchange on the magnetic-resonance spectrum of alkali vapors

W. Happer, A. C. Tam

It was recently discovered that when there are sufficiently rapid spin-exchange collisions in an alkali-metal vapor, the rf magnetic-resonance frequency of the ground-state atoms becomes a constant fractional value (e.g., $\frac{4}{11}$ for Cs) of the Larmor frequency, and the linewidth becomes inversely proportional to the spin-exchange rate. These properties are in complete contrast to those in the slow spin-exchange limit. We present a theoretical analysis of these properties, and we predict some additional new effects for rapid spin exchange. Four theories are presented; an intuitive-vector model, a perturbation treatment, numerical solutions of complex non-Hermitian matrices, and a statistical analysis of the effect of rapid transfers between two Zeeman multiplets. These theories all provide, to varying degrees, consistent quantitative answers to the problem of how spin exchange affects magnetic resonance in an alkali vapor.

Physical Review A•Nov 1, 1977•292 citations
Coherence transfer between atomic levels requires the matching of the Larmor frequencies. For levels with different ggg factors this occurs only in zero magnetic field. By changing the ggg factors through coupling with a nonresonant rf field, one can match the Larmor frequencies and make the transfer possible in nonzero magnetic fields. Resonances in the transfer appear, depending on the rf field amplitude. Rb87{\mathrm{Rb}}^{87}Rb87-Cs133{\mathrm{Cs}}^{133}Cs133 spin-exchange experiments are reported which provide an illustration of the theory.
In spin-related fundamental researches, there have been considerable interests in the transfer of microscopic orders between magnetic sublevels of different kinds of atoms. As for gaseous atomic systems, collisional transfer of spin polarization from optically pumped atoms A to atoms B is attained through spin exchange collisions. So far many experiments have been reported on the transfer of longitudinal spin polarization created along a static magnetic field. Transfer of coherence, on the other hand,is possible only when the energy matching condition j!A !Bj < is satisfied, where !A and !B are the Larmor frequencies of atoms A and B, and the line width. This is the reason why transfer of spin polarization precessing around the static magnetic field has not been observed except for a few experiments; The coherence transfer has been observed in the experiments where the atoms are subjected to properly chosen rf magnetic fields. Recently, it has been reported that coherence transfer between different kinds of atoms is possible by using the light field which transversely pumps only one kind of atoms under properly chosen experimetal conditions. It has also been pointed out that, as for the system of Rb and K atoms, which happen to have the same gyro-magnetic ratio, the peculier distortion of the magnetic resonance signal line shapes observed in the collisionally pumped atoms can be explained by the spin exchange coupling between the resonant Rb and K atoms. It is suggested that the precessing spin polarization in Rb can be transferred to K atoms or vice versa, since their Zeeman splittings become equal in the hyperfine multiplets jF 1⁄4 1i and jF 1⁄4 2i of the ground state 2S1=2 with the same gyromagnetic ratio 1⁄4 2 700 kHz/G. The experimental apparatus of the present experiment is shematically shown in Fig. 1. In addition to a droplet of natural rubidium and potassium, the sample cell contains 50mbar Ar as a buffer gas. It is subjected to a static magnetic field of H0 1⁄4 0:786G along the z axis and irradiated transversely to the field by a light beam from a GaAlAs laser A (output power = 10mW, beam diameter = 1mm). It is left-handed circularly polarized and tuned to the Rb absorption lines (S1=2, F 1⁄4 1 ! P1=2, F 1⁄4 1 and 2) which are not resolved owing to the Doppler broadening. The intensity of the laser A is modulated by an AOM (acousto-optic-modulator) at the Larmor frequency !A 1⁄4 2 550 (1⁄4 700 0:786) kHz of Rb in a rectangular shape pulse. As mentioned above the precessing spin polarization in Rb can be transferred to K. The precessing spin polarization of Rb and that of K are detected from the Faraday rotations of the beams of probe lasers B ( 1⁄4 794 nm, output power = 3mW, beam diameter = 2mm) and C ( 1⁄4 769 nm, output power = 3mW, beam diameter = 2mm), respectively. The frequency of laser B is chosen to be a few GHz higher than the Rb absorption lines (S1=2, F 1⁄4 1 ! P1=2, F 1⁄4 1 and 2) to prevent the detection beam from destroying the polarization. Similarly, the frequency of laser C is chosen to be a few GHz higher than the K absorption lines (S1=2, F 1⁄4 1 and 2 ! P1=2, F 1⁄4 1 and 2) which are not resolved owing to the Doppler broadening. They are linearly polarized and counter-propagated against the pumping beam,making angles of about 1 to the pumping beam. In each case the transmitted light beam of probe laser passes through the analyzer which makes an angle 45 to the polarization of the incident beam,and then it is detected by a pin-photo diode. The signals are electronically averaged over a few hundred cycles. Figure 2(a) shows the typical examples of signals on the magnetizations M x and M B x of Rb and K, respectively, Fig. 1. Schematic diagram of the experimetal apparatus. AOM, acoustooptic modulator; PD, pin-photo diode; P, polarizer; A, analyzer.
We study the interactions between oscillating nonresonant rf fields and atoms with strong spin-exchange collisions in the presence of a weak dc magnetic field. We find that the atomic Larmor precession frequency shows a new functional form to the rf field parameters when the spin-exchange collision rate is tuned. In the weak rf field amplitude regime, a strong modification of atomic Larmor frequency appears when the spin-exchange rate is comparable to the rf field frequency. This effect has been neglected before due to its narrow observation window. We compare the experimental results with density matrix calculations, and explain the data by an underdamped oscillator model. When the rf field amplitude is large, there is a minimum atomic gyromagnetic ratio point due to the rf photon dressing, and we find that strong spin-exchange interactions modify the position of such a point.
A rigorous quantum theory of atomic collisions in the presence of radio frequency (rf) magnetic fields is developed and applied to elucidate the effects of combined dc and rf magnetic fields on ultracold collisions of Rb atoms. We show that rf fields can be used to induce Feshbach resonances, which can be tuned by varying the amplitude and frequency of the rf field. The rf-induced Feshbach resonances occur also in collisions of atoms in low-field-seeking states at moderate rf field strengths easily available in atom chip experiments, which opens up the world of tunable interactions to magnetically trappable atomic quantum gases.
Radio-frequency (rf) fields in the MHz range are used to induce resonant energy transfer between cold Rydberg atoms in spatially separated volumes. After laser preparation of the Rydberg atoms, dipole-dipole coupling excites the 49s49s49s atoms in one cylinder to the 49p49p49p state while the 41d41d41d atoms in the second cylinder are transferred down to the 42p42p42p state. The energy exchanged between the atoms in this process is 33GHz33\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}33GHz. An external rf field brings this energy transfer into resonance. The strength of the interaction has been investigated as a function of amplitude (0−−1V∕cm)(0--1\phantom{\rule{0.3em}{0ex}}\mathrm{V}∕\mathrm{cm})(0−−1V∕cm) and frequency (1−−30MHz)(1--30\phantom{\rule{0.3em}{0ex}}\mathrm{MHz})(1−−30MHz) of the rf field and as a function of a static-field offset. Multiphoton transitions up to fifth order as well as selection rules prohibiting the process at certain fields have been observed. The width of the resonances has been reduced compared to earlier results by switching off external magnetic fields of the magneto-optical trap, making sub-MHz spectroscopy possible. All features are well reproduced by theoretical calculations taking the strong ac Stark shift due to the rf field into account.
It was recently discovered that when there are sufficiently rapid spin-exchange collisions in an alkali-metal vapor, the rf magnetic-resonance frequency of the ground-state atoms becomes a constant fractional value (e.g., 411\frac{4}{11}114​ for Cs) of the Larmor frequency, and the linewidth becomes inversely proportional to the spin-exchange rate. These properties are in complete contrast to those in the slow spin-exchange limit. We present a theoretical analysis of these properties, and we predict some additional new effects for rapid spin exchange. Four theories are presented; an intuitive-vector model, a perturbation treatment, numerical solutions of complex non-Hermitian matrices, and a statistical analysis of the effect of rapid transfers between two Zeeman multiplets. These theories all provide, to varying degrees, consistent quantitative answers to the problem of how spin exchange affects magnetic resonance in an alkali vapor.