FREQUENCY STANDARD BASED ON COHERENT POPULATION

TRAPPING (CPT)

FIELD OF THE INVENTION

The present invention relates in general to the field of frequency standards, and in particular, to miniature atomic clocks that operate by probing coherent population trapping (CPT) resonances using linearly polarized light for decreasing populating dilution of the m _F =0 states.

BACKGROUND OF THE INVENTION

Atomic clocks based on coherent population trapping (CPT) spectroscopy implemented by miniature and low power consuming devices provide for various applications, such as in the field of navigation and communication. US Patent 6,806,784, the entire content of which is hereby incorporated as a reference, discloses an atomic clock based on CPT excitation technique. The clock comprises frequency-modulated laser, such as a vertical cavity surface-emitting laser (VCSEL), illuminating a collection of atomic absorbers, such as alkali atoms, contained in a micro-machined cell. Laser current modulation at a frequency that equals half of the frequency corresponding to the hyperfine split of the ground state of the absorbers produces the optical sideband used for CPT. The changes in the transmitted power of the illuminating laser beam through the cell are used to stabilize an external oscillator corresponding to the transition frequency of the absorbers.

Reference is now made to Figs. 1 A - 1C in which a schematic setup for measuring CPT resonance, an exemplary energy scheme and an exemplary transmission profile according to prior art are respectively shown. Absorbers

contained in cell 10 are illuminated with light beam having at least two components frequencies matching the CPT resonance and a beam axis 12. Light detector 14 detects light transmitted through cell 10 along axis 16. The energy scheme of the absorbers consists of at least two energy levels 21 and 22 corresponding to two of the ground states respectively, coupled to common energy level 22 by illuminating components 24 and 25 having frequencies vi and V ₂ respectively. Energy difference 26 separates between the two ground states corresponding to a third frequency V _f . Transmission profile 30 measured by this setup, such that V ₁ is held constant and by varying the second frequency, has a maximum at V _f . The CPT resonance is characterized by its full width half maximum 32, δv, and its height 34, h, often stated in terms of the absorption contrast, C=h/absorption, where the absorption is indicated by the depth 36 of the average value of the transmitted power external to the CPT resonance. These two parameters determine how effectively the resonance can be used to define a specific frequency for a clock. Narrow, high-contrast resonances imply improved frequency stability.

US Patent 6,888,780 discloses a method and system employing CPT resonances associated with end states (namely sublevels of maximal or minimal azimuthal quantum numbers) to stabilize the frequency of the atomic clock. Alkali metal vapor is pumped with circularly-polarized laser light that is either intensity-modulated at resonance frequencies, or having constant- intensity and simultaneously applied with alternating magnetic fields oscillating at respective Zeeman frequencies. As a result a significant portion of the alkali atoms are concentrated in the initial state of the resonances, contrary to the "population dilution" normally associated with CPT resonances. Such "end resonances" have much stronger signals than the 0 - 0 resonance associated with decreased spin exchange broadening which dominates the line-width of the 0 -0 resonance.

US Patent application 2005/0212607 discloses a method and system for increasing the intensity of CPT resonances, used in atomic clocks, by employing light of alternating circular polarization to pump the atoms. Such light is characterized by . a spin vector of the photons that alternates in

direction at a hyperfine frequency of the atoms thereby exciting transitions in which the azimuthal quantum number is correspondingly changed by a unit. Such resonances are significantly enhanced by an optically induced concentration of atoms in the resonant energy sublevels.

The enhanced stability of the optically pumped atomic clocks according to these last disclosures is associated with a complexity associated with either the introduction of the alternating magnetic field, the intensity modulation of the laser light, or the changing of its polarization, at appropriate frequencies. A solution providing for an enhanced clock stability that is less complex is therefore beneficial.

BRIEF DESCRIPTION OF THE DRAWINGS

Fig. 1A is a schematic setup for measuring a CPT resonance according to prior ART; Fig. 1 B is an exemplary energy scheme providing for a CPT resonance to be measured by the setup shown in Fig. 1 A;

Fig. 1C is a plot of the photo power detected versus the difference between frequencies of two components of the illuminating light shown in Fig. 1A; Fig. 2 is a simplified block diagram of a frequency standard according to the present invention;

Fig. 3 schematically shows transitions among Zeeman sublevels of the hyperfine structure of the S1/2 and P1/2 states of ⁸⁷ Rb states;

Fig. 4 is a schematic presentation of a segment of a frequency standard according to a preferred embodiment of the present invention;

Fig. 5 is a graph comparing between two typical synthetic transmittances of the absorbers, one of which is calculated according to the present invention and the other in accordance with a frequency standard of the prior art; Fig. 6 is a histogram presenting an exemplary population of the energy levels calculated for the same known frequency standard of Fig. 5;

Fig. 7 is a histogram presenting an exemplary population of the same energy levels shown in Fig. 6 calculated in accordance with the present invention;

DETAILED DESCRIPTION OF THE PRESENT INVENTION

In accordance with the present invention a frequency standard having substantially improved accuracy and stability is provided. Reference is first made to Fig. 2 in which a simplified block diagram of a frequency standard according to the present invention is shown. As in the prior art, miniature vapor cell 50 containing vapors of absorber such as atoms of alkali metal optionally mixed with a buffer gas is illuminated by light beam 52 ₅ which is circularly polarized. Exemplary current driven VCSEL 54 modulated by oscillator 56 and a suitable circular polarizer implement such source of light beam providing for exciting coherent population trapping (CPT) resonances of these absorbers. Means for measuring photo power 58 measures the power of light transmitted through cell 50. The power of the transmitted light changes with the frequency of oscillator 56. These changes provide for stabilizing the oscillator frequency as known. A low magnitude magnetic field, such as of a few milli Gauss, provides for defining the azimuthal quantum numbers of the absorbers. A solenoid attached to the walls of cell 50, not shown, induces a substantially homogeneous magnetic field across cell 50 directed along axis 60 of light beam 52.

According to the present invention linearly polarized light beam 62, propagates perpendicularly to the magnetic field to illuminate the absorbers contained in cell 50. This light beam is emitted from a source having for example one or two VCSELs, not shown, such modulated that their spectrum includes frequencies corresponding to F, rri _F → F =F, m' _F =m _F transitions; where F is the angular momentum corresponding to the vector sum of the electronic spin and the nuclear spin of the absorbers, ITIF is the respective azimuthal quantum number, namely the respective component of F along the magnetic field. Such transitions provide according to the present invention for populating the two states corresponding to the ground levels F=1 ,2, ITIF=0, thereby enhancing the above-mentioned CPT resonances. The stabilized frequency of

oscillator 56 constitute the frequency standard according to the present invention. Reference is made to Fig. 3 in which such exemplary transitions are shown. Arrows 90 indicate transitions between levels in which F=F=2 and m=m' whereas arrows 92 indicate transitions between levels in which F=F=I .

Reference is now made to Fig. 4 in which segment 100 of a frequency standard according to a preferred embodiment of the present invention is schematically shown. Miniature vapor cell 102 contains absorbers such as isotopically pure rubidium ⁸⁷ Rb and a buffer gas such as nitrogen and or any combination of noble gases as known. Vapor cell 102 whose volume is of a few cubic millimeters is enclosed within magnetic shield 104 such as made of foils of mumetal. Two left or right circularly polarized light beams represented by light rays 106, which copropogate, illuminate a volume enclosed within vapor cell 102. The light beams are emitted by current modulate VCSEL 108. Collimating lens or lenses 110 collimates the light emitted from VCSEL 108, which is further circularly polarized by means of a suitable quarter wave length plate (QWP) 112. Electric current generated by generator 114 and further modulated by an RF oscillator whose frequency range is tuned to half the hyperfine frequency gap of the Rb ground state, such as oscillator 116, feeds the VCSEL. Light detector 118, such as a silicon photo diode, measures the intensity of light transmitted through vapor cell 102. The signals received by light detector 118 are further employed for controlling the frequency of oscillator 116 as known. Solenoid 120 provides for generating a substantially homogeneous magnetic field directed along the axis of the illuminating beams. Optionally two orthogonal solenoids perpendicularly disposed to solenoid 120, not shown, provide for canceling the residual magnetic field. The light beam indicated by light rays 122 is linearly polarized in the same direction of the magnetic field generated by solenoid 120. The source of this light beam includes current driven VCSEL, the current generator and the oscillator feeding it, collimating and polarizing means. Collimating lens or lenses 124 collimates the light emitted from VCSEL 126, which is further linearly polarized by polarizer 128. Current generated by generator 130 and modulated by RF oscillator 132 feeds VCSEL 126. The frequency range of oscillator 132 which is of about 3

GHz complies with the energy gaps corresponding to the above-mentioned F=F', m=m' transitions. Oscillator 132 can be less accurate than oscillator 116 since it provides for single photon transitions.

EXAMPLE

A computer program modeled a frequency standard according to a preferred embodiment of the invention, as is shown in Fig. 4, and its operation was simulated accordingly. The modeled vapor cell contains isotopically pure ⁸⁷ Rb. The modeled circularly polarized light frequencies comply with D1 transitions as known. The computerized model was calibrated by matching calculated transmittance values and respective contrasts, with and without modulating intensities of the circularly polarized light and or the magnitude of the magnetic field, with known respective values of contrasts and transmittances when the linearly polarized light beam was not operative. The respective calculated values reasonably complied with known respective values.

Reference is now made to Figs 5 - 7 in which graphs comparing between the transmittance values of the vapor cell and the populations of respective energy levels of the absorbers are respectively presented when calculated according to the invention and in accordance with the prior art. Curve 140 represents the transmittance of the vapor cell when calculated for ⁸⁷ Rb as a function of the difference between the frequency of the illuminating light, which is circularly polarized, and half of the respective resonance frequency. In accordance with the present invention the beam of linearly polarized light whose frequency is modulated concomitantly illuminates the rubidium atoms. Curve 142 represent the transmittance as a function of the

same frequencies' differences calculated when only the circularly polarized light beams illuminate the vapor cell as known. The origin of the frequency scale corresponds to 3.417 GHz. The contrast calculated for curve 140 is more than four times larger than the contrast corresponding to curve 142. Hence improved accuracies and stabilities are provided by a frequency standard according to the present invention.

In Fig. 6 the population distribution calculated for F=1 and F=2 in their respective ITIF levels according to prior art is shown at the resonance frequency. In Fig. 7 the population distribution of the same energy levels is shown in a case in which pumping by utilizing linearly polarized light at the resonance frequency is induced. Such pumping is referred hereinafter by π pumping. The heights of the bars of the histograms shown are proportional to the relative population of respective levels. These simulated results substantiate that π pumping according to the invention result in a significantly larger population in the UIF=O levels providing for the higher contrast values achieved.