Patent Application: US-201214002583-A

Abstract:
the frequency of an atomic clock may be stabilized against c - field variation by applying a rf magnetic field perpendicular to the c - field to cause a coherent population transfer between zeeman states that compensates for quadratic frequency shift of transitions of the clock . the cancellation , provided by a feed - forward mechanism , is exact . the invention can be implemented in any atomic clock by including an electrode in the clock generating a magnetic field perpendicular to the c - field , and providing an electronic circuit to send rf signals to the electrode .

Description:
fig1 is a schematic diagram of a “ physics package ” of a standard atomic clock . a source of cesium atoms 1 produces an atomic beam 2 directed along the longitudinal axis of the clock . the source produces atoms distributed between the possible atomic states | f , m f & gt ;. a “ first state selector ” 3 transmits the atoms which are in any of the states | 3 , m f & gt ; and rejects the atoms in the | 4 , m f & gt ; states ( the cesium atom is used for the discussion ). using a microwave cavity , a first microwave field 5 imposes a π / 2 - pulse at the hyperfine transition frequency between states | 3 , 0 & gt ; and | 4 , 0 & gt ; ( also called the 0 - 0 transition or the clock transition ). the result is an atomic state - superposition oscillating at the frequency of the 0 - 0 transition . the atoms drift in a region of constant and uniform magnetic field until they are imposed a second microwave π / 2 - pulse in the second microwave field 6 — this is the ramsey technique of time - separated microwave fields ( ramsey 1950 ). after exiting the second microwave field , the atoms will be in the | 4 , 0 & gt ; state if the frequency of the microwave field is equal to the frequency of the 0 - 0 transition . a second state selector 4 transmits the atoms which are in any of the states | 4 , m f & gt ; and rejects the atoms in the | 3 , m f & gt ; states . these atoms reach the detector 7 and produce a microwave ramsey signal . the constant and uniform magnetic field in the region between 5 and 6 , called the c - field , is produced with a constant current flowing through the c - field electrodes 8 and 9 . the c - field is parallel to the magnetic component of the microwave fields 5 and 6 . a magnetic shield ( not shown ) encloses the c - field region to provide the maximum isolation from variations of external fields . fig2 shows a typical microwave ramsey signal ( called ramsey fringes ) obtained from the detector 7 in fig1 as a function of the frequency f mw of the microwave field . the abscissa shows the difference between f mw and the frequency of the 0 - 0 transition f 00 , with zero centered on the graph . when the frequency f mw is equal to the frequency of the 0 - 0 transition , the microwave ramsey signal reaches a maximum . fig3 shows a schematic diagram of the electronics package of an atomic clock . a local oscillator determines the clock rate . its frequency is stable but not accurate , and thus requiring an adjustment . the signal from this local oscillator is used by the microwave frequency synthesizer to generate a microwave signal at a frequency near f 00 . the two frequencies of fig2 a and b are generated by adding and subtracting the frequency of the signal generated by the offset frequency generator . a modulator alternately selects frequencies a and b in synchronism with the output signal from a modulation frequency generator . the output of the modulator is sent to the microwave cavity . the microwave ramsey signal from the detector is sent to the demodulator part of a servo control . the servo control adjusts the frequency of the local oscillator to keep the microwave ramsey signals measured at points a and b equal . the technique keeps the frequency of the local oscillator precisely locked to the frequency of the 0 - 0 transition , and thus the rate of the clock remains very stable . however , the frequency of all atomic transitions is a function of the magnetic field ( zeeman effect ), which implies that the clock rate is affected by the value of the c - field . fig4 shows the dependence of the atomic state frequency on the magnetic field for a cesium atom . for small magnetic fields ( smaller than 40 mt in cesium ), all but the 0 - 0 transitions have a linear frequency dependence on the magnetic field ( zeeman splitting ). the 0 - 0 transition is the transition with the smallest ( but non - null ) frequency sensitivity on the c - field . in order to keep the frequency of the clock as constant as possible , special care must be taken to produce a uniform c - field which will be stable over extended periods of time . a variation of the c - field away from its nominal value b 0 produces a shift of the ramsey fringe δ r = c 1 ∫( b 2 ( z )− b 0 2 ) dz , where b ( z ) is the value of the c - field at position z integrated along the trajectory between the two microwave ramsey excitations , and c 1 is a constant determined by atomic properties ( c 1 is equal to 42 . 745 mhz / μt 2 in cesium ). for small variations of the c - field away from its nominal value ( b ( z )− b 0 & lt ;& lt ; b 0 ) the frequency shift of the microwave ramsey fringe is δ r = 2b 0 c 1 ∫( b ( z )− b 0 ) dz . the frequency shift of a zeeman transition between the δm f =± 1 states is given by δ z = c 2 ∫( b ( z )− b 0 ) dz , where c 2 is a constant determined by atomic properties ( c 2 is equal to 3 . 5 khz / μt in cesium ). thus , we can express the frequency shift of the ramsey fringe δ r = 2b 0 c 1 δ z / c 2 = εδ z . two rf magnetic pulses at a control frequency f c and tuned near the zeeman frequency f z = c 2 ∫ b ( z ) dz are added to the c - field . this is to produce a small population transfer between the δf = 0 , δm f =± 1 states . the two rf pulses are an implementation of the ramsey technique using rf magnetic fields using the circuit shown in fig6 . thus , this technique uses a rf ramsey interrogation within a microwave ramsey interrogation . the frequency of the rf signal is also modulated in synchronism with the microwave modulation , and so part of the signal from the detector has the dependence shown in fig2 , with the abscissa showing f c − f z = f c − c 2 ∫ b ( z ) dz . since the zeeman frequency shift is much larger than the ramsey shift ( δ z / δ r is equal to 1 / ε = 6820 for a typical field of 6 μt in a commercial cesium beam clock ), the rf pulses need only to have a small amplitude such that only a small fraction of the population is transferred . such an rf ramsey signal is confirmed experimentally ( marmet 2011 ) and is shown in fig1 . the states of interest for the microwave ramsey interrogation are the states | 3 , 0 & gt ; and | 4 , 0 & gt ; ( the notation | f , m f & gt ; is used ). since the rf magnetic pulses have a small amplitude , these two states connect to the states | 3 , − 1 & gt ;, | 3 , 1 & gt ;, | 4 , − 1 & gt ; and | 4 , 1 & gt ;. the contribution from the other states is negligible and not considered in this discussion . here , we use non - normalized populations to describe the populations in each state a 3 - 1 | 3 , − 1 & gt ;, a 30 | 3 , 0 & gt ;, a 31 | 3 , 1 & gt ;, a 4 - 1 | 4 , − 1 & gt ;, a 40 | 4 , 0 & gt ; and a 41 | 4 , 1 & gt ;, and ρ 3 - 1 =| a 3 - 1 | 2 ρ 30 =| a 30 | 2 , ρ 31 =| a 31 | 2 , ρ 4 - 1 =| a 4 - 1 | 2 , ρ 40 =| a 40 | 2 , and ρ 41 =| a 41 | 2 . fig9 shows a diagram of the atomic populations , with cesium being used as an example . fig9 a : after the first state selector , only the atoms with populated | 3 , m f & gt ; states are transmitted . the populations are and ρ 3 - 1 = ρ 30 = ρ 31 = 1 and ρ 4 - 1 = ρ 40 = ρ 41 = 0 . fig9 b : the first microwave ramsey pulse produces a coherent state - superposition between the states | 3 , 0 & gt ; and | 4 , 0 & gt ;, with ρ 3 - 1 = ρ 31 = 1 , ρ 4 - 1 = ρ 41 = 0 , and ρ 30 = ρ 40 = 0 . 5 . fig9 c : the first rf ramsey pulse produces several coherent state - superposition between the following states : | 3 , − 1 & gt ; and | 3 , 0 & gt ;, | 3 , 1 & gt ; and | 3 , 0 & gt ;, | 4 , − 1 & gt ; and | 4 , 0 & gt ;, and | 4 , 1 & gt ; and | 4 , 0 & gt ;. the resulting populations are ρ 3 - 1 = ρ 31 = 1 − 3ε / 8 , ρ 30 = 0 . 5 + ε / 4 , ρ 4 - 1 = ρ 41 = ε / 8 and ρ 40 = 0 . 5 − ε / 4 . the value of ε is related to the amplitude of the rf magnetic field and is kept small ( of the order of δ r / δ z ). fig9 d : the second rf ramsey pulse , is phase shifted by δ / 2 ( that is , the rf frequency tuned to points a or b on fig2 ) and produces more population transfers between the states : | 3 , − 1 & gt ; and | 3 , 0 & gt ;, | 3 , 1 & gt ; and | 3 , 0 & gt ;, | 4 , − 1 & gt ; and | 4 , 0 & gt ;, and | 4 , 1 & gt ; and | 4 , 0 & gt ;. the resulting populations are ρ 30 = 0 . 5 + εr ( f c − f z ), ρ 4 - 1 = ρ 41 = εr ( f c − f z )/ 2 and ρ 40 = 0 . 5 − εr ( f c − f z ), where r ( f c − f z ) is the ramsey function plotted in fig2 . fig9 e : the second microwave ramsey pulse produces more population transfer between the states | 3 , 0 & gt ; and | 4 , 0 & gt ;, resulting in the populations ρ 4 - 1 = ρ 41 = εr ( f c − f z )/ 2 and ρ 40 = r ( f mw − f 00 ). fig9 f : after the second state selector , only the atoms with populated | 4 , m f & gt ; states are transmitted , resulting in the populations ρ 3 - 1 = ρ 30 = ρ 31 = 0 , ρ 4 - 1 = ρ 41 = εr ( f c − f z )/ 2 , and ρ 40 = r ( f mw − f 00 ). finally , the detector measures the total population resulting in a signal s = ρ 3 - 1 + ρ 30 + ρ 31 + ρ 4 - 1 + ρ 40 + ρ 41 = r ( f mw − f 00 )+ εr ( f c − f z ). eq . ( 1 ) ( without rf pulses ( e . g . ε = 0 , prior art ), the detected signal would be s 0 = r ( f mw − f 00 ).) the feedback signal s is calculated by using the function r ( f ) at the two operating points fig2 a and b . near these points , the function can be simplified to the linear relation ( first order taylor expansion ) r ( f )= ½ + β ( δf ± f ), where δf is the offset frequency , the “−” is for point a on fig2 , and “+” is for point b on fig2 . in order to compensate the frequency shift of the 0 - 0 transition , the contribution from the rf ramsey signal is made negative by using a modulation which is out of phase with respect to the microwave modulation ( e . g . when the microwave frequency is at point a , the rf frequency is at point b , and vice versa .) the signal is then s =± β [( f clock − f 00 )− ε ( f c − f z )]+( 1 + ε )( ½ + βδ f ). f z − f c = c 2 ∫ b ( z ) dz − c 2 ∫ b 0 dz = δ z = δ r c 2 /( 2 b 0 c 1 ), s =± β [ f clock − δ r ( 1 − εc 2 /( 2 b 0 c 1 ))]+ k , where k is a constant . the servo control modifies f clock in order to keep the signal s constant . the value of δ r depends on the c - field , but with the choice ε = 2b 0 c 1 / c 2 it is multiplied by zero , therefore removing the dependence of the signal s on the value of the c - field . thus , by selecting the amplitude of the rf pulses so that ε = 2b 0 c 1 / c 2 , the frequency shift of the rf ramsey signal will cancel the frequency shift of the microwave ramsey signal . the small value of ε & lt ; 0 . 0002 needed for this method is to be contrasted to the large population transfer ( effectively 100 % or ε = 1 ) used in the “ multi - coherent method ” ( happer 2008 ) where the m f = 0 , ± 1 , ± 2 , etc . states are completely mixed by large rf signals . with the appropriate selection of the rf pulses amplitude , the rf ramsey signal added to the microwave ramsey fringes ( the error signal steering the frequency of the clock ) cancels and c - field deviation away from the nominal value determined by the frequency of the rf oscillations f c . since the c - field is sampled by each atom along its individual trajectory ( as represented by the integral ∫ b ( z ) dz ), spatial variations of the c - field are cancelled as well as temporal variations . thus , there is provided a method of stabilizing the frequency of an atomic clock against c - field non - uniformity and temporal variations by applying rf magnetic pulses perpendicular to the c - field to cause a coherent population transfer between zeeman states that compensates for the quadratic frequency shift of transitions of the clock . thus , the rf magnetic pulses produce a compensation directly at the level of the frequency servo loop . no feedback based on a measurement of the c - field has to be applied to the c - field dc current . the dc current producing the c - field does not need to be actively modified , the microwave synthesizer circuit need not be modified from prior art and no additional measurement cycle is necessary . this can improve the stability of a clock by a large factor ( e . g . by a factor of five or more ) against changes of the c - field without changing other aspects of the clock . leaving other aspects of the clock alone is a desirable practice when working with standards , especially when long term stability is important . the present invention may be implemented in any atomic clock , for example a fountain clock or a beam clock . the atomic species used for the frequency reference must have the proper spectroscopic structure , such an alkali metal standard ( e . g . a cesium standard or a rubidium standard ). it is an advantage of the present invention that its implementation in an atomic clock is relatively straightforward and inexpensive . implementation requires only a few excitation electrodes to be added to the central part of an existing clock design , preferably inside all metal layers since the rf magnetic field is cancelled by conductors . embodiment # 1 : excitation electrodes producing a transversal field over the entire region of the c - field referring to fig7 , a first embodiment of an atomic clock in accordance with the present invention has many of the same features as a standard atomic clock including source of cesium atoms 11 , atomic beam 12 , 1 st state selector 13 , 1 st microwave field 15 , 2 nd microwave field 16 , 2 nd state selector 14 , detector 17 and c - field electrodes 18 and 19 . in this embodiment , a series of pulses are generated regularly , spaced in time so that a pair of pulses fits within the time between the two microwave ramsey excitations . two additional “ excitation electrodes ” 20 and 21 produce a magnetic field which is transversal ( in relation to the axis of atomic beam 12 ) and perpendicular to the c - field , over the entire length between microwave pulses 15 and 16 . the signal sent to the excitation electrodes is generated with the circuit depicted in fig6 . the pulses are shown in fig5 , where the time between two microwave ramsey excitations is equal to 1 on the abscissa . depending on their position , the atoms are subjected to one or two rf magnetic pulses . most atoms are subjected to only one rf pulse during the time between the microwave ramsey pulses . however , the atoms receiving the first rf magnetic pulse just after the first ramsey pulse will be subjected to two rf pulses . for those atoms , the method is applicable . with rf pulses as shown in fig5 , about 10 % of the atoms participate to the rf ramsey signal . the smaller signal can be compensated by using a value for ε ten times larger . embodiment # 2 : excitation electrodes producing a longitudinal field over two short sections near the microwave excitation regions referring to fig8 , a second embodiment of an atomic clock in accordance with the present invention has many of the same features as a standard atomic clock including source of cesium atoms 31 , atomic beam 32 , 1 st state selector 33 , 1 st microwave field 35 , 2 nd microwave field 36 , 2 nd state selector 34 , detector 37 and c - field electrodes 38 and 39 . in this embodiment , a constant rf magnetic field is produced but since the rf fields are localized , the atoms experience two pulses between the two microwave ramsey excitations . two additional “ excitation electrodes ” 40 and 41 produce a magnetic field which is longitudinal ( parallel to the atomic beam ) and perpendicular to the c - field , over short lengths near the microwave excitation fields 35 and 36 . the signal sent to the excitation electrodes is generated with the circuit depicted in fig6 . the temporal pulses experienced by the atoms are shown in fig5 , where the time between two microwave ramsey excitations is equal to 1 on the abscissa . all atoms are subjected to two rf magnetic pulses and the method is applicable as described above with a small value of ε . embodiment # 3 : a clock with an atomic source producing atoms only in the state ( 3 , 0 & gt ;, e . g . some fountain clocks in this embodiment , the electrode set - ups of embodiment # 1 or # 2 can be used . in this case , the method uses the small difference between the zeeman frequency splitting between the | 3 , m f & gt ; states and the splitting between the | 4 , m f & gt ; states . the constant c 2 used above is specific to the value of f , e . g . c 2 ( f = 3 )= 3509 . 8 hz / μt and c 2 ( f = 4 )= 3498 . 6 hz / μt in cesium . after the first state selector , the populations are ρ 30 = 1 , and ρ 3 - 1 = ρ 31 = ρ 4 - 1 = ρ 40 = ρ 41 = 0 . the first microwave ramsey pulse produces a coherent state - superposition between the states | 3 , 0 & gt ; and | 4 , 0 & gt ;, giving ρ 3 - 1 = ρ 31 = ρ 4 - 1 = ρ 41 = 0 and ρ 30 = ρ 40 = 0 . 5 . the first rf ramsey pulse produces the populations ρ 3 - 1 = ρ 31 = ρ 4 - 1 = ρ 41 = ε / 8 and ρ 30 = ρ 40 = 0 . 5 − ε / 4 . the value of ε is related to the amplitude of the rf magnetic field and is kept small ( of the order of δ r / δ z ). the second rf ramsey pulse , is phase shifted by π / 2 ( that is , the rf frequency tuned to points a or b on fig2 ). the resulting populations are ρ 30 = 0 . 5 + εr ( f c − f z3 ), ρ 4 - 1 = ρ 41 = εr ( f c − f z4 )/ 2 and ρ 40 = 0 . 5 − εr ( f c − f z4 ), where r ( f c − f zf ) is the ramsey function plotted in fig2 and f zf is f z calculated with the constants c 2 ( f ). the second microwave ramsey pulse produces the populations ρ 4 - 1 = ρ 41 = εr ( f c − f z4 )/ 2 and ρ 40 = r ( f mw − f 00 )− ε [ r ( f c − f z3 )+ r ( f c − f z4 )]/ 2 . after the second state selector , only the atoms with populated | 4 , m f & gt ; states are transmitted , resulting in ρ 3 - 1 = ρ 30 = ρ 31 = 0 . finally , the detector measures the total population resulting in a signal s = ρ 3 - 1 + ρ 30 + ρ 31 + ρ 4 - 1 + ρ 40 + ρ 41 = r ( f mw − f 00 )+ ε [ r ( f c − f z4 )− r ( f c − f z3 )]/ 2 . the feedback signal s is used in the same way as the signal of eq . ( 1 ), except that here the correction term r ( f c − f z4 )− r ( f c − f z3 ) provides the sensitivity on the c - field to be used as a first - order correction to the second - order zeeman shift . references : the contents of the entirety of each of which are incorporated by these references . barnes j a , rodrigo e a . ( 1988 ) “ fine tuning of atomic frequency standards ,” u . s . pat . no . 4 , 740 , 761 issued apr . 26 , 1988 . braun a m , abeles j h , kwakernaak m , davis t j . ( 2010 ) “ batch - fabricated , rf - interrogated , end transition , chip - scale atomic clock ”. u . s . pat . no . 7 , 852 , 163 issued dec . 14 , 2010 . de marchi a ., “ the high c - field concept for an accurate cesium beam resonator ,” proc . 7 th european frequency and time forum , neuchâtel , switzerland , march 1993 . happer w , jau y y , gong f . 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( 1990 ) “ atomic clock ,” u . s . pat . no . 4 , 943 , 955 issue jul . 24 , 1990 . ramsey n . f . ( 1950 ) “ a molecular beam resonance method with separated oscillating fields ,” physical review , vol . 78 , issue 6 : 695 - 699 ; jun . 15 , 1950 . rubiola e , del casale a , de marchi a . ( 1993 ) “ a dual frequency synthesis scheme for a high c field cesium resonator .” proceedings of the 47 th ieee international frequency control symposium . 105 , 1993 . stern a , levy b , bootnik m , detoma e , pedrotto g . ( 1992 ) “ rubidium frequency standard with a high resolution digital synthesizer .” proceedings of the 46 th ieee international frequency control symposium . 108 , 1992 . stern a , levy b . ( 2003 ) “ atomic frequency standard and system having improved long term aging .” u . s . pat . no . 6 , 614 , 321 issued sep . 2 , 2003 . other advantages that are inherent to the structure are obvious to one skilled in the art . the embodiments are described herein illustratively and are not meant to limit the scope of the invention as claimed . variations of the foregoing embodiments will be evident to a person of ordinary skill and are intended by the inventor to be encompassed by the following claims .