Patent Number: 
Section: claims

1. A method for determining a total velocity average cross-section parameter σtotν in a relationship of the form Γloss(U)=nbσtotν·ƒ(U, Ud), where: Γloss(U) is a rate of exponential loss of sensor atoms from a cold atom sensor trap of trap depth potential energy U in a vacuum environment due to collisions with residual particles in the vacuum environment; nb is a number density of residual particles in the vacuum environment; Ud is a parameter given by      U    d    =                    2        ⁢                                  ⁢                  k          B                ⁢        T        ⁢                  /                ⁢                  m          bg                      ⁢                  4        ⁢                                  ⁢        π        ⁢                            2                                      m          t                ⁢                  〈                                    σ              tot                        ⁢            v                    〉                    which relates masses of the sensor atoms mt and residual particles mbg to the total velocity average cross-section parameter σtotν; and ƒ(U, Ud) is a function of the trap depth potential energy U and the parameter Ud which models a naturally occurring dependence of the loss rate Γloss(U) on the trap depth potential energy U and the parameter Ud, where ƒ(U=0, Ud) is unity for all Ud, the method comprising:for a particular species pair comprising the sensor atoms and the residual particles, iterating a process which comprises in each iteration: varying the trap depth potential energy U for the cold atom sensor trap in which the sensor atoms are trapped; and measuring the loss rate Γloss(U) of the sensor atoms from the cold atom sensor trap;after a plurality of iterations of the process, extrapolating the measured loss rate Γloss(U) data to obtain an estimate of Γloss(U=0);determining the total velocity average cross-section parameter σtotν wherein determining the total velocity average cross-section parameter σtotν comprises performing a curve fitting process to fit                              Γ          loss                ⁡                  (          U          )                                      Γ          loss                ⁡                  (                      U            =            0                    )                      =                            〈                                    σ              loss                        ⁢            v                    〉                          〈                                    σ              tot                        ⁢            v                    〉                    =              f        ⁡                  (                      U            ,                          U              d                                )                      ,where σlossνis velocity averaged cross-section of the particular species pair at a given trap depth potential energy U, to solve for the total velocity average cross-section parameter σtotν. 2. A method according to claim 1 wherein performing the curve fitting process to fit                    Γ        loss            ⁡              (        U        )                            Γ        loss            ⁡              (                  U          =          0                )              =                    〈                              σ            loss                    ⁢          v                〉                    〈                              σ            tot                    ⁢          v                〉              =          f      ⁡              (                  U          ,                      U            d                          )            to solve for the total velocity average cross-section parameter σtotν comprises:expressing ƒ(U, Ud) as ƒ(U, σtotν) based on            U      d        =                            2          ⁢                                          ⁢                      k            B                    ⁢          T          ⁢                      /                    ⁢                      m            bg                              ⁢                        4          ⁢                                          ⁢          π          ⁢                                  2                                                m            t                    ⁢                      〈                                          σ                tot                            ⁢              v                        〉                                ;andperforming the curve fitting process to solve directly for the total velocity average cross-section parameter σtotν. 3. A method according to claim 1 wherein performing the curve fitting process to fit                    Γ        loss            ⁡              (        U        )                            Γ        loss            ⁡              (                  U          =          0                )              =                    〈                              σ            loss                    ⁢          v                〉                    〈                              σ            tot                    ⁢          v                〉              =          f      ⁡              (                  U          ,                      U            d                          )            to solve for the total velocity average cross-section parameter σtotν comprises:performing the curve fitting process to fit                    Γ        loss            ⁡              (        U        )                            Γ        loss            ⁡              (                  U          =          0                )              =                    〈                              σ            loss                    ⁢          v                〉                    〈                              σ            tot                    ⁢          v                〉              =          f      ⁡              (                  U          ,                      U            d                          )            to thereby determine the parameter Ud; anddetermining the total velocity average cross-section parameter σtotνaccording to      〈                  σ        tot            ⁢      v        〉    =                    2        ⁢                                  ⁢                  k          B                ⁢        T        ⁢                  /                ⁢                  m          bg                      ⁢                            4          ⁢                                          ⁢          π          ⁢                                  2                                                m            t                    ⁢                      U            d                              .       4. A method according to claim 1 wherein the model function ƒ(U, Ud) has a form of a polynomial expansion in a variable      (          U              U        d              )    . 5. A method according to claim 1 wherein the model function ƒ(U, Ud) has a form of (1−pQM), where      p    QM    =            ∑              j        =        1            J        ⁢                            β          j                ⁡                  (                      U                          U              d                                )                    j      where J is an integer greater than 1 and βj are parameters of the model function ƒ(U, Ud). 6. A method according to claim 5, wherein pQM represents a probability that a sensor atom stays in the cold atom sensor trap after a collision with a residual particle. 7. A method according to claim 5, wherein the parameters βj of the model function ƒ(U, Ud) are determined based on a theoretical model of collisions between the sensor atoms and the residual particles. 8. A method according to claim 5 wherein the parameters βj of the model function ƒ(U, Ud) are experimentally determined. 9. A method for determining a number density nb of second residual particles in a second vacuum environment comprising second sensor atoms trapped in a second cold atom sensor trap of trap depth potential energy U*, the method comprising:using the total velocity average cross-section parameter σtotν determined in accordance with the method of claim 1 wherein the second sensor atoms are the same as the sensor atoms and the second residual particles are the same as the residual particles;measuring a loss rate Γloss(U=U*) of the second sensor atoms from the second cold atom sensor trap at the trap depth potential energy U*; anddetermining the number density nb of second residual particles in the second vacuum environment according to nb=Γloss(U*)/[σtotν·ƒ(U=U*, Ud)]. 10. A method according to claim 9 wherein the second vacuum environment is the same as the vacuum environment and the second cold atom trap is the same as the cold atom trap. 11. A method according to claim 9 wherein the second vacuum environment is different from the vacuum environment and the second cold atom trap is different from the cold atom trap. 12. A method according to claim 9 wherein the model function ƒ(U, Ud) has a form of (1−pQM), where      p    QM    =            ∑              j        =        1            J        ⁢                            β          j                ⁡                  (                      U                          U              d                                )                    j      where J is an integer greater than 1 and βj are parameters of the model function ƒ(U, Ud). 13. A method for calibrating an ionization gauge which measures a pressure Pb of second residual particles in a second vacuum environment comprising second sensor atoms trapped in a second cold atom sensor trap of trap depth potential energy U*, the method comprising:using the total velocity average cross-section parameter σtotν determined in accordance with the method of claim 1 wherein the second sensor atoms are the same as the sensor atoms and the second residual particles are the same as the residual particles;measuring a loss rate Γloss(U=U*) of the second sensor atoms from the second cold atom sensor trap at the trap depth potential energy U*;measuring the pressure Pb of the second residual particles in the second vacuum environment using the ionization gauge at the same trap depth potential energy U*; anddetermining a calibration factor ig for the ionization gauge according to:      i    g    =                              P          b                ⁢                  〈                                    σ              tot                        ⁢            v                    〉                                      (                                    k              B                        ⁢            T                    )                ⁢                              Γ            loss                    ⁡                      (            U            )                                ⁢                  f        ⁡                  (                                    U              =                              U                *                                      ,                          U              d                                )                    .       14. A method according to claim 13 wherein the second vacuum environment is the same as the vacuum environment and the second cold atom trap is the same as the cold atom trap. 15. A method according to claim 13 wherein the second vacuum environment is different from the vacuum environment and the second cold atom trap is different from the cold atom trap. 16. A method according to claim 13 wherein the model function ƒ(U, Ud) has a form of (1−pQM), where      p    QM    =            ∑              j        =        1            J        ⁢                            β          j                ⁡                  (                      U                          U              d                                )                    j      where J is an integer greater than 1 and βj are parameters of the model function ƒ(U, Ud). 17. A method for calibrating an ionization gauge which measures a pressure Pb of second residual particles in a second vacuum environment comprising second sensor atoms trapped in a second cold atom sensor trap of trap depth potential energy U*, the method comprising:using the number density nb of second residual particles in the second vacuum environment determined in accordance with the method of claim 9 wherein the second sensor atoms are the same as the sensor atoms and the second residual particles are the same as the residual particles;measuring a loss rate Γloss(U=U*) of the second sensor atoms from the second cold atom sensor trap at the trap depth potential energy U*;measuring the pressure Pb of the second residual particles in the second vacuum environment using the ionization gauge at the same trap depth potential energy U*; anddetermining a calibration factor ig for the ionization gauge according to:      i    g    =                    P        b                              n          b                ⁡                  (                                    k              B                        ⁢            T                    )                      .   18. A method according to claim 17 wherein the second vacuum environment is the same as the vacuum environment and the second cold atom trap is the same as the cold atom trap. 19. A method according to claim 17 wherein the second vacuum environment is different from the vacuum environment and the second cold atom trap is different from the cold atom trap. 20. A method according to claim 17 wherein the model function ƒ(U, Ud) has a form of (1−pQM), where      p    QM    =            ∑              j        =        1            J        ⁢                            β          j                ⁡                  (                      U                          U              d                                )                    j      where J is an integer greater than 1 and βj are parameters of the model function ƒ(U, Ud). 21. A method for calibrating a mass spectrometer which measures a signal Sb corresponding to second residual particles in a second vacuum environment comprising second sensor atoms trapped in a second cold atom sensor trap of trap depth potential energy U*, the method comprising:using the total velocity average cross-section parameter σtotν determined in accordance with the method of claim 1 wherein the second sensor atoms are the same as the sensor atoms and the second residual particles are the same as the residual particles;measuring a loss rate Γloss(U=U*) of the second sensor atoms from the second cold atom sensor trap at the trap depth potential energy U*;measuring a signal Sb corresponding to the second residual particles in the second vacuum environment using the mass spectrometer at the same trap depth potential energy U*; anddetermining a calibration factor is for the mass spectrometer according to:      i    s    =                              S          b                ⁢                  〈                                    σ              tot                        ⁢            v                    〉                                      (                                    k              B                        ⁢            T                    )                ⁢                              Γ            loss                    ⁡                      (            U            )                                ⁢                  f        ⁡                  (                                    U              =                              U                *                                      ,                          U              d                                )                    .       22. A method for calibrating a mass spectrometer which measures a signal Sb of second residual particles in a second vacuum environment comprising second sensor atoms trapped in a second cold atom sensor trap of trap depth potential energy U*, the method comprising:using the number density nb of second residual particles in the second vacuum environment determined in accordance with the method of claim 9 wherein the second sensor atoms are the same as the sensor atoms and the second residual particles are the same as the residual particles;measuring a loss rate Γloss(U=U*) of the second sensor atoms from the second cold atom sensor trap at the trap depth potential energy U*;measuring a signal Sb corresponding to the second residual particles in the second vacuum environment using the mass spectrometer at the same trap depth potential energy U*; anddetermining a calibration factor is for the mass spectrometer according to:      i    s    =                    S        b                              n          b                ⁡                  (                                    k              B                        ⁢            T                    )                      .   23. A method for determining number densities n1,2,3, . . . of a plurality of second residual particles in a second vacuum environment comprising second sensor atoms trapped in a second cold atom sensor trap, the method comprising:for each of the plurality of second residual particles, using the total velocity average cross-section parameter σtotν determined in accordance with the method of claim 1 wherein the second sensor atoms are the same as the sensor atoms and the second residual particles are the same as the residual particles, to thereby obtain a plurality of total velocity average cross-section parameters σtotν1,2,3, . . . corresponding to the plurality of second residual particles;iterating a process which comprises in each iteration:varying the trap depth potential energy U for the cold atom sensor trap in which the sensor atoms are trapped; andmeasuring the loss rate Γloss(U) of the sensor atoms from the cold atom sensor trap;to thereby obtain a plurality of loss rates Γloss1,2,3, . . . (U1,2,3, . . . ) at different trap depth potential energies U1,2,3, . . . , the plurality of loss rates Γloss1,2,3, . . . (U1,2,3, . . . ) greater than or equal to the plurality of second residual particles;determining corresponding values of Ud1,2,3, . . . for the second residual particles according to            U              d                  1          ,          2          ,          3          ,          …                      =                            2          ⁢                                          ⁢                      k            B                    ⁢          T          ⁢                      /                    ⁢                      m            bg                              ⁢                        4          ⁢                                          ⁢          π          ⁢                                  2                                                m            t                    ⁢                                    〈                                                σ                  tot                                ⁢                v                            〉                                      1              ,              2              ,              3              ,              …                                            ;solving a system of equations having the form:                                          Γ            loss                    ⁡                      (                          U              1                        )                          =                                            n              1                        ⁢                                                            〈                                                            σ                      tot                                        ⁢                    v                                    〉                                1                            ⁡                              [                                  1                  -                                                            ∑                                              j                        =                        1                                            N                                        ⁢                                                                                            β                          j                                                ⁡                                                  (                                                                                    U                              1                                                                                      U                                                              d                                ⁢                                                                                                                                  ⁢                                1                                                                                                              )                                                                    j                                                                      ]                                              +                                    n              2                        ⁢                                                            〈                                                            σ                      tot                                        ⁢                    v                                    〉                                2                            ⁡                              [                                  1                  -                                                            ∑                                              j                        =                        1                                            N                                        ⁢                                                                                            β                          j                                                ⁡                                                  (                                                                                    U                              1                                                                                      U                                                              d                                ⁢                                                                                                                                  ⁢                                2                                                                                                              )                                                                    j                                                                      ]                                              +                                    n              3                        ⁢                                                            〈                                                            σ                      tot                                        ⁢                    v                                    〉                                3                            ⁡                              [                                  1                  -                                                            ∑                                              j                        =                        1                                            N                                        ⁢                                                                                            β                          j                                                ⁡                                                  (                                                                                    U                              1                                                                                      U                                                              d                                ⁢                                                                                                                                  ⁢                                3                                                                                                              )                                                                    j                                                                      ]                                              +          …                                    (                  13          ⁢          A                )                                                      Γ            loss                    ⁡                      (                          U              2                        )                          =                                            n              1                        ⁢                                                            〈                                                            σ                      tot                                        ⁢                    v                                    〉                                1                            ⁡                              [                                  1                  -                                                            ∑                                              j                        =                        1                                            N                                        ⁢                                                                                            β                          j                                                ⁡                                                  (                                                                                    U                              2                                                                                      U                                                              d                                ⁢                                                                                                                                  ⁢                                1                                                                                                              )                                                                    j                                                                      ]                                              +                                    n              2                        ⁢                                                            〈                                                            σ                      tot                                        ⁢                    v                                    〉                                2                            ⁡                              [                                  1                  -                                                            ∑                                              j                        =                        1                                            N                                        ⁢                                                                                            β                          j                                                ⁡                                                  (                                                                                    U                              2                                                                                      U                                                              d                                ⁢                                                                                                                                  ⁢                                2                                                                                                              )                                                                    j                                                                      ]                                              +                                    n              3                        ⁢                                                            〈                                                            σ                      tot                                        ⁢                    v                                    〉                                3                            ⁡                              [                                  1                  -                                                            ∑                                              j                        =                        1                                            N                                        ⁢                                                                                            β                          j                                                ⁡                                                  (                                                                                    U                              2                                                                                      U                                                              d                                ⁢                                                                                                                                  ⁢                                3                                                                                                              )                                                                    j                                                                      ]                                              +          …                                    (                  13          ⁢          B                )                                                                    Γ              loss                        ⁡                          (                              U                3                            )                                =                                                    n                1                            ⁢                                                                    〈                                                                  σ                        tot                                            ⁢                      v                                        〉                                    1                                ⁡                                  [                                      1                    -                                                                  ∑                                                  j                          =                          1                                                N                                            ⁢                                                                                                    β                            j                                                    ⁡                                                      (                                                                                          U                                3                                                                                            U                                                                  d                                  ⁢                                                                                                                                          ⁢                                  1                                                                                                                      )                                                                          j                                                                              ]                                                      +                                          n                2                            ⁢                                                                    〈                                                                  σ                        tot                                            ⁢                      v                                        〉                                    2                                ⁡                                  [                                      1                    -                                                                  ∑                                                  j                          =                          1                                                N                                            ⁢                                                                                                    β                            j                                                    ⁡                                                      (                                                                                          U                                3                                                                                            U                                                                  d                                  ⁢                                                                                                                                          ⁢                                  2                                                                                                                      )                                                                          j                                                                              ]                                                      +                                          n                3                            ⁢                                                                    〈                                                                  σ                        tot                                            ⁢                      v                                        〉                                    3                                ⁡                                  [                                      1                    -                                                                  ∑                                                  j                          =                          1                                                N                                            ⁢                                                                                                    β                            j                                                    ⁡                                                      (                                                                                          U                                3                                                                                            U                                                                  d                                  ⁢                                                                                                                                          ⁢                                  3                                                                                                                      )                                                                          j                                                                              ]                                                      +            …                          ⁢                                  ⁢                                                                                                              ⁢                ⋮                                                    ⋮                                      ⋮                                                          (                  13          ⁢          C                )            to thereby obtain the number densities n1,2,3, . . . of the plurality of second residual particles in the second vacuum environment.