Techniques for using chirped fields to reconfigure a medium that stores spectral features

Claim 3

A method as recited in claim 1 , wherein: the chirped electromagnetic field further includes a start edge in a start time interval T S adjacent before the erasure time interval T E ; and an amplitude A S of the electromagnetic field oscillations during the start time interval T S increases with a substantively continuous first derivative from substantively zero at a start of the start time interval T S to A E and a substantively zero rate of change at an end of the start time interval T S .

Claim 4

A method as recited in claim 2 , wherein a frequency ω(t) of the electromagnetic field oscillations at a time t during the start time interval T S changes with a substantively continuous first derivative to match a start frequency ω 0 and start frequency rate of change κ S at a start of the erasure time interval T E .

Claim 5

A method as recited in claim 2 , wherein a phase of the electromagnetic field oscillations during the start time interval T S changes with a substantively continuous first derivative to match a start phase and start phase rate of change at a start of the erasure time interval T E .

Claim 6

A method as recited in claim 2 , wherein A S is substantively specified by an equation of form A S ( t )={cosine [π( t−t 0 )/ T S ]+1 }A E /2, in which t is time and t 0 is time at a start of the erasure time interval T E .

Claim 7

A method as recited in claim 3 , wherein ω(t) during the start time interval T S is substantively specified by an equation of form d ω( t )/ dt ={cosine [π( t−t 0 )/ T S ]+1}κ s/ 2, in which t is time, t 0 is time at a start of the erasure time interval T E , dω(t)/dt is time rate of change of frequency at a time t, and κs is the start frequency rate of change at time t 0 .

Claim 8

A method as recited in claim 1 , wherein: the chirped electromagnetic field further includes a finish edge in a finish time interval T F adjacent after the erasure time interval T E ; and an amplitude A F of the electromagnetic field oscillations during the finish time interval T F decreases with a substantively continuous first derivative from a value substantively equal to A E with a substantively zero rate of change at a start of the finish time interval T F to zero at an end of the finish time interval T F .

Claim 9

A method as recited in claim 7 , wherein a frequency ω(t) of the electromagnetic field oscillations at a time t during the finish time interval T F changes with a substantively continuous first derivative to match an end-erase frequency ωe and an end-erase frequency rate of change κe at an end of the erasure time interval T E .

Claim 10

A method as recited in claim 7 , wherein a phase of the electromagnetic field oscillations during the finish time interval T F changes with a substantively continuous first derivative to match an end-erase phase and an end-erase phase rate of change at an end of the erasure time interval T E .

Claim 11

A method as recited in claim 7 , wherein A F is substantively specified by an equation of form A F ( t )={cosine [π( t−t 0 −T E )/ T F ]+1 }A E /2, in which t is time and to is time at a start of the erasure time interval T E .

Claim 12

A method as recited in claim 8 , wherein ω(t) during the finish time interval T F is substantively specified by an equation of form d ω( t )/ dt ={cosine [π( t−t 0 −T E )/ T F ]+1}κ e/ 2, in which t is time, t 0 is time at a start of the erasure time interval T E , dω(t)/dt is time rate of change of frequency at a time t, and κe is the end-erase frequency rate of change at the end of the erasure time interval T E .

Claim 13

A method as recited in claim 1 , wherein the chirp rate κ is substantively constant over the erasure frequency band and substantively equal to B E /T E .

Claim 14

A method as recited in claim 2 , wherein: the chirped electromagnetic field further includes a finish edge in a finish time interval T F adjacent after the erasure time interval T E ; and an amplitude A F of the electromagnetic field oscillations during the finish time interval T F decreases with a substantively continuous first derivative from a value substantively equal to A E with a substantively zero rate of change at a start of the finish time interval T F to zero at an end of the finish time interval T F .

Claim 15

A method as recited in claim 13 , wherein a duration of the start time interval T S is substantively equal to a duration of the finish time interval T F .

Claim 16

A method as recited in claim 1 , wherein the amplitude A E of the electromagnetic field oscillations over the bandwidth B E is substantively constant and substantively specified by the equation for a particular portion less than all of the medium, in which portion spectral features are to be erased.

Claim 17

A method as recited in claim 1 , wherein the medium is an inhomogeneously broadened transition (IBT) material and the amplitude A E and dipole moment μ are for an electric field.

Claim 18

A method as recited in claim 1 , wherein the medium is a material subjected to a magnetic field for nuclear magnetic resonance (NMR) measurements and the amplitude A E and dipole moment μ are for a magnetic field.

Claim 19

A method as recited in claim 1 , further comprising the step of causing a different chirped electromagnetic field to pass into the medium, wherein: the different chirped electromagnetic field has a monochromatic frequency that varies in time by a chirp rate κ2 over a different erasure frequency band of bandwidth B E2 during the same erasure time interval T E ; and an amplitude A E2 of the electromagnetic field oscillations in the different chirped electromagnetic field over the bandwidth B E2 is substantively constant and substantively specified by an equation of form A E2 =( h bar/μπ)√{square root over ((κ2 ln 2))} whereby substantively fifty percent of the two-state atomic system responsive in the different erasure frequency band exposed to the different chirped electromagnetic field is in the first state after erasure regardless of a percentage in the first state before erasure.

Claim 20

A method as recited in claim 1 , further comprising: in response to causing the chirped electromagnetic field to pass into the medium, receiving a readout electromagnetic field from the medium; and determining the spectral features stored in the medium within the erasure frequency band before erasure based on the readout electromagnetic field.

Claim 21

A method as recited in claim 1 , wherein: interactions of the chirped electromagnetic field and the medium are coherent over a time scale up to time T 2 ; and the chirp rate κ within the erasure frequency band satisfies an inequality given by κ>>ln 2/(π T 2 ) 2 , whereby erasure is effective even at small values for T 2 .

Claim 22

A method as recited in claim 1 , wherein: the medium is an optical absorption medium with frequency-dependent absorption based on the two state atomic system; the two-state atomic system has a population decay time that describes a rate of return of a population of atoms in the two-state atomic system to a ground state of the two state atomic system; and the method further comprises waiting a particular time based on a target absorption value and the population decay time, whereby absorption over the erasure frequency band attains the target absorption value.

Claim 23

A method as recited in claim 3 , wherein ω(t) during the start time interval T S is substantively specified by an equation of form d ω( t )/ dt=κs in which t is time, dω(t)/dt is time rate of change of frequency at a time t, and κs is the start frequency rate of change at a start of the erasure time interval T E .

Claim 24

A method as recited in claim 22 , wherein: κ is a constant substantively equal to B E /T E ; and κs is substantively equal to κ.

Claim 25

A method as recited in claim 8 , wherein ω(t) during the finish time interval T F is substantively specified by an equation of form d ω( t )/ dt=κe in which t is time, dω(t)/dt is time rate of change of frequency at a time t, and κe is the end-erase frequency rate of change at the end of the erasure time interval T E .

Claim 26

A method as recited in claim 24 , wherein: κ is a constant substantively equal to B E /T E ; and κe is substantively equal to κ.

Claim 29

A method as recited in claim 26 , wherein: the chirped electromagnetic field further includes a start edge in a start time interval T S adjacent before the inversion time interval T I ; and an amplitude A S of the electromagnetic field oscillations during the start time interval T S increases with a substantively continuous first derivative from substantively zero at a start of the start time interval T S to A I and a substantively zero rate of change at an end of the start time interval T S .

Claim 30

A method as recited in claim 27 , wherein a frequency ω(t) of the electric field oscillations at a time t during the start time interval T S changes with a substantively continuous first derivative to match a start frequency ωs and start frequency rate of change κs at a start of the inversion time interval T I .

Claim 31

A method as recited in claim 27 , wherein a phase of the electromagnetic field oscillations during the start time interval T S changes with a substantively continuous first derivative to match a start phase and start phase rate of change at a start of the inversion time interval T I .

Claim 32

A method as recited in claim 27 , wherein A S is substantively specified by an equation of form A S ( t )={sec h [( t−t 0 )/( T S /2)]} A I , in which t is time and t 0 is time at a start of the erasure time interval T I and sech is the hyperbolic secant function.

Claim 33

A method as recited in claim 28 , wherein ω(t) during the start time interval T S is substantively specified by an equation of form ω( t )=ω 0 +{T S tan h [( t−t 0 )/( T S /2)]− T I }κs/ 2, in which t is time, to is time at a start of the inversion time interval T I , ω 0 is frequency at time t 0 , κs is the start frequency rate of change at time t 0 , and tanh is the hyperbolic tangent function.

Claim 34

A method as recited in claim 26 , wherein: the chirped electromagnetic field further includes a finish edge in a finish time interval T F adjacent after the inversion time interval T I ; and an amplitude A F of the electromagnetic field oscillations during the finish time interval T F decreases with a substantively continuous first derivative from a value substantively equal to A I with a substantively zero rate of change at a start of the finish time interval T F to zero at an end of the finish time interval T F .

Claim 35

A method as recited in claim 32 , wherein a frequency ω(t) of the electromagnetic field oscillations at a time t during the finish time interval T F changes with a substantively continuous first derivative to match an end-invert frequency ω 0 +B I and an end-invert frequency rate of change κe at an end of the inversion time interval T I .

Claim 36

A method as recited in claim 32 , wherein a phase of the electromagnetic oscillations during the finish time interval T F changes with a substantively continuous first derivative to match an end-invert phase and an end-invert phase rate of change at an end of the inversion time interval T I .

Claim 37

A method as recited in claim 32 , wherein A F is substantively specified by an equation of form A F ( t )={sec h [( t−t 0 −T I )/( T F /2)]} A I , in which t is time and to is time at a start of the inversion time interval T I .

Claim 38

A method as recited in claim 33 , wherein ω(t) during the finish time interval T F is substantively specified by an equation of form ω( t )=ω 0 +{T S tan h [( t−t 0 −T I )/( T S /2)]+ T I }κe/ 2, in which t is time, t 0 is time at a start of the inversion time interval T I , ω 0 is frequency at time t 0 , and κe is the end-invert frequency rate of change at the end of the inversion time interval T I .

Claim 39

A method as recited in claim 26 , wherein the chirp rate κ is substantively constant over the inversion frequency band and substantively equal to B I /T I .

Claim 40

A method as recited in claim 27 , wherein: the chirped electromagnetic field further includes a finish edge in a finish time interval T F adjacent after the inversion time interval T I ; and an amplitude A F of the electromagnetic field oscillations during the finish time interval T F decreases with a substantively continuous first derivative from a value substantively equal to A I with a substantively zero rate of change at a start of the finish time interval T F to zero at an end of the finish time interval T F .

Claim 41

A method as recited in claim 38 , wherein the start time interval T S is substantively equal to the finish time interval T F .

Claim 42

A method as recited in claim 26 , wherein the amplitude A I of the electromagnetic field oscillations over the inversion frequency band is substantively constant and substantively specified by the equation for a particular portion less than all of the medium in which portion spectral features are to be inverted.

Claim 43

A method as recited in claim 26 , wherein the medium is an inhomogeneously broadened transition (IBT) material and the amplitude A I and dipole moment μ are for an electric field.

Claim 44

A method as recited in claim 26 , wherein the medium is a material subjected to a magnetic field for nuclear magnetic resonance (NMR) measurements and the amplitude A I and dipole moment μ are for a magnetic field.

Claim 45

A method as recited in claim 26 , further comprising the step of causing a different chirped electromagnetic field to pass into the medium, wherein: the different chirped electromagnetic field has a monochromatic frequency that varies in time by a chirp rate κ2 over a different inversion frequency band of bandwidth B I2 during the same inversion time interval T I ; and an amplitude A I2 of the electromagnetic field oscillations in the different chirped electromagnetic field over the bandwidth B I2 is substantively constant and substantively specified by an equation of form A I2 =( h bar/μπ)√{square root over ((κ2 ln [2/ε2]))} in which ε2 is a non-zero fractional difference from complete inversion whereby a particular relative population (r) of the excited state of the two-state atomic system, responsive at a particular frequency in the inversion frequency band exposed to the chirped electromagnetic field, is substantively equal to X*(1−ε) after inversion when the relative population of the excited state is −X before inversion, wherein r is +1 to indicate all atoms are in the excited state and r is −1 to indicate all atoms are in the ground state.

Claim 46

A method as recited in claim 26 , wherein: interactions of the chirped electromagnetic field and the medium are coherent over a time scale up to time T 2 ; and the chirp rate κ within the inversion frequency band satisfies an inequality given by κ>>ln [2/ε]/(π T 2 ) 2 , whereby inversion is effective even at small values for T 2 .

Claim 47

A method as recited in claim 26 , wherein: the medium is an optical absorption medium with frequency-dependent absorption based on the two state atomic system; the two-state atomic system has a population decay time that describes a rate of return of a population of atoms in the two-state atomic system to a ground state of the two state atomic system; and the method further comprises waiting a particular time based on a target absorption value and the population decay time, whereby absorption over the inversion frequency band attains the target absorption value.

Claim 48

A method as recited in claim 28 , wherein ω(t) during the start time interval T S is substantively specified by an equation of form d ω( t )/ dt=κs in which t is time, dω(t)/dt is time rate of change of frequency at a time t, and κs is the start frequency rate of change at a start of the inversion time interval T I .

Claim 49

A method as recited in claim 46 , wherein: κ is a constant substantively equal to B I /T I ; and κs is substantively equal to κ.

Claim 50

A method as recited in claim 33 , wherein ω(t) during the finish time interval T F is substantively specified by an equation of form d ω( t )/ dt=κe in which t is time, dω(t)/dt is time rate of change of frequency at a time t, and κe is the end-erase frequency rate of change at the end of the inversion time interval T I .

Claim 51

A method as recited in claim 48 , wherein: κ is a constant substantively equal to B I /T I ; and κe is substantively equal to κ.

Claim 56

A computer-readable medium carrying one or more sequences of instructions for forming chirped electromagnetic field to reconfigure spectral features stored in a medium based on a two-state atomic system having a transition dipole moment of μ, in which an atom transitions between a first state and a second state, wherein execution of the one or more sequences of instructions by one or more processors causes the one or more processors to perform the steps of: determining a temporal frequency form for a chirped electromagnetic field that includes a monochromatic frequency that varies in time by a chirp rate κ over a reconfiguration frequency band of bandwidth B R during a reconfiguration time interval T R ; and determining an amplitude A R of electromagnetic field oscillations in the chirped electromagnetic field over the reconfiguration frequency band that is substantively constant and substantively specified by an equation of form A R =( h bar/μπ)√{square root over ((κ ln [2/ε]))}, in which hbar is reduced Plank's constant, ln is a natural logarithm function, π is a ratio of a circumference of a circle to a diameter of the circle; and driving an electromagnetic modulator to impose the chirped electromagnetic field onto an electromagnetic carrier frequency, whereby for ε<<1, a particular relative population (r) of the excited state of the two-state atomic system, responsive at a particular frequency in the inversion frequency band exposed to the chirped electromagnetic field, is substantively equal to X*(1−ε) after inversion when the relative population of the excited state is −X before inversion, wherein r is +1 to indicate all atoms are in the excited state and r is −1 to indicate all atoms are in the ground state, and for ε=1, substantively fifty percent of the two-state atomic system responsive in the erasure frequency band exposed to the chirped electromagnetic field is in the first state after erasure regardless of a percentage in the first state before erasure.

Claim 57

A computer-readable medium carrying one or more sequences of instructions for forming chirped electromagnetic field to reconfigure spectral features stored in a medium based on a two-state atomic system having a transition dipole moment of μ, in which an atom transitions between a first state and a second state, wherein execution of the one or more sequences of instructions by one or more processors causes the one or more processors to perform the steps of: determining a temporal frequency form for a chirped electromagnetic field that includes a monochromatic frequency that varies in time by a chirp rate κ over a reconfiguration frequency band of bandwidth B R during a reconfiguration time interval T R ; and determining an amplitude A R of electromagnetic field oscillations in the chirped electromagnetic field over the reconfiguration frequency band that is substantively constant and substantively specified by an equation of form A R =( h bar/μπ)√{square root over ((κ ln [2/ε]))}, in which hbar is reduced Plank's constant, ln is a natural logarithm function, π is a ratio of a circumference of a circle to a diameter of the circle; and driving an electromagnetic modulator to impose the chirped electromagnetic field onto an electromagnetic carrier frequency, whereby for ε<<1, a particular relative population (r) of the excited state of the two-state atomic system, responsive at a particular frequency in the inversion frequency band exposed to the chirped electromagnetic field, is substantively equal to X*(1−ε) after inversion when the relative population of the excited state is −X before inversion, wherein r is +1 to indicate all atoms are in the excited state and r is −1 to indicate all atoms are in the ground state, and for ε=1, substantively fifty percent of the two-state atomic system responsive in the erasure frequency band exposed to the chirped electromagnetic field is in the first state after erasure regardless of a percentage in the first state before erasure.