The present invention relates to devices that utilize coherent population trapping to determine the resonance frequency associated with two energy levels in a quantum absorber.
To simplify the following discussion, the present invention will first be explained in terms of a frequency standard. Other applications of the invention will then be discussed below. High-speed communication links that operate at modulation frequencies above 1 GHz have become common in telecommunications and other digital communication links. Such systems have created a need for inexpensive frequency standards that can operate outside the standards laboratory. Such a frequency standard must provide a reliable output signal independent of environmental fluctuations such as temperature and magnetic fields.
One class of frequency standard that has the potential for meeting these needs utilizes Coherent-Population-Trapping (CPT) in quantum absorbers. CPT-based frequency standards are described in U.S. Pat. Nos. 6,363,091 and 6,201,821, which are hereby incorporated by reference. Since such frequency standards are known to the art, they will not be described in detail here. For the purposes of the present discussion, it is sufficient to note that in such standards, the output of an electromagnetic source that has two frequency components (CPT-generating frequency components) that are separated by a frequency difference is applied to a quantum absorber. The quantum absorber has at least two low energy states and at least one high energy state that can be reached by transitions from each of the low energy states. One of these two CPT-generating frequency components in the applied electromagnetic field induces transition from one of the low energy states to the high energy state while the other frequency component induces the transition from the other low energy state to the common high energy state. Thus the quantum absorber absorbs the energy from the applied electromagnetic field.
When the frequency difference between the two frequency components is approximately the same as the corresponding frequency difference between two low energy states in the quantum absorber, the quantum absorber can be in a linear superposition of the two low energy states such that the quantum absorber does not interact with the applied electromagnetic field. This phenomenon is called Coherent-Population-Trapping (CPT). The quantum absorber exhibits an absorption minimum (or a transmission maximum) when the frequency difference between the two frequency components is exactly the same as the corresponding frequency difference between two low energy states in the quantum absorber. A suitable detector measures the intensity of the electromagnetic field transmitted through the quantum absorber. A servo loop can be used to adjust the frequency difference of these two frequency components such that the maximum amount of electromagnetic field leaves the quantum absorber. Hence, the frequency difference of these two frequency components is held at a precise value that is related to the difference in energy of the corresponding low energy states of the quantum absorber. If the difference in energy of the low states in the absorber remains constant, the resultant frequency standard will have a very high precision.
In some frequency standards, a modulated laser is used to produce the CPT-generating frequency components. One or more sidebands from the modulation can be used as the CPT-generating frequency components. In this case, the servo-loop mentioned above controls the frequency difference between the CPT-generating frequency components by adjusting the modulation frequency. Since the modulation frequency generator is held at a frequency determined by the low states of the absorber, the output of the modulation frequency generator provides a frequency standard having high precision provided the difference in energy of the corresponding low energy states of the quantum absorber remains constant.
As noted above, to be useful as a CPT-based frequency standard, the device must be insensitive to environmental conditions. Since the CPT is induced by the applied electromagnetic field at the frequencies corresponding to the transition frequencies from the low energy states to the common high energy state, the absorber often exhibits an AC Stark shift. As a result, the energy difference between the two low energy states will vary as a function of the intensity of the CPT-generating frequency components applied to the quantum absorber.
One method for reducing the AC Stark shift operates by introducing additional frequency components (AC-Stark-shift-manipulating frequency components) into the applied electromagnetic field. If the AC-Stark-shift-manipulating frequency components have the correct intensities and frequencies relative to the intensities of the CPT-generating frequency components discussed above, the AC Stark shift is substantially reduced. In this case, the difference in energy between the two low states will be insensitive to the intensities of the CPT-generating frequency components. If a modulated laser is used to generate the CPT-generating frequency components, the intensities of the AC-Stark-shift-manipulating frequency components are readily changed by adjusting the amplitude of the modulation signal applied to the laser. The frequencies of the AC-Stark-shift-manipulating frequency components are determined by the modulation frequency. In this example, both the CPT-generating frequency components and the AC-Stark-shift-manipulating frequency components are generated by modulating the same laser; the ratio of intensity of any one frequency component to any other frequency component is determined by the modulation. Therefore the AC Stark shift is insensitive to the total incidence intensity of the laser beam.
While the inclusion of the AC-Stark-shift-manipulating frequency components substantially corrects the problems introduced by the AC Stark shift, the AC-Stark-shift-manipulating frequency components reduce the signal-to-noise ratio in the output of the detector used to measure the intensity of electromagnetic radiation transmitted through the quantum absorber. Hence, these components reduce the effectiveness of the servo loop that corrects for variations in the frequency difference between the CPT-generating frequency components. The reduction in signal-to-noise ratio results from a difference in absorption between the CPT-generating frequency components and the AC-Stark-shift-manipulating frequency components. The AC-Stark-shift-manipulating frequency components suffer much less absorption in the quantum absorber than the two CPT-generating frequency components. Since the detector measures the sum of the powers of each of the frequency components in the electromagnetic field transmitted through the quantum absorber, the power in these AC-Stark-shift-manipulating frequency components forms a more or less constant background signal that is superimposed on the signal represented by the variation in the intensities of the two CPT-generating frequency components as the frequency difference between them is varied. This background signal reduces the signal-to-noise ratio.
The present invention includes a CPT detector having a quantum absorber, polarization analyzer and detector. The quantum absorber includes a material having first and second low energy states coupled to a common high energy state. Transitions between the first low energy state and the common high energy state and between the second low energy state and the common high energy state are induced by electromagnetic radiation having a first polarization. The first polarization is altered to a second polarization when the electromagnetic radiation passes through the quantum absorber. The polarization analyzer preferentially blocks electromagnetic radiation having a polarization state different from the second polarization state. The polarization analyzer is irradiated with a portion of an electromagnetic signal that has passed through the quantum absorber. The detector generates a signal related to the intensity of electromagnetic radiation that leaves the polarization analyzer.
In one embodiment, the CPT detector also includes an electromagnetic radiation source that generates electromagnetic radiation having CPT-generating frequency components for generating CPT, and additional frequency components for reducing an AC Stark shift in the quantum absorber. The CPT-generating frequency components differ in frequency by 2ν. The CPT-generating frequency components have the first polarization state. The generated electromagnetic radiation irradiates the quantum absorber. A controller alters ν in response to the generated signal from the detector. A signal having a frequency determined by ν is also generated in embodiments in which the CPT detector is used as a frequency standard.
In another embodiment, the electromagnetic radiation source includes a first electromagnetic radiation generator that generates electromagnetic radiation at a frequency equal to νL and an oscillator for generating a modulation signal having a frequency ν. The modulating signal modulates the electromagnetic radiation from the first electromagnetic radiation source to generate a modulated electromagnetic radiation signal. The CPT generator may also include a polarization synthesizer for causing the modulated electromagnetic radiation signal to have the first polarization.
In yet another embodiment, the electromagnetic radiation source includes a laser for generating a first light signal having a third polarization state and a tunable oscillator for generating a signal that modulates the first light signal. A quarter waveplate for altering the third polarization state to the first polarization state may also be included.
The manner in which the present invention provides its advantages can be more easily understood with reference to
The optical spectrum generated by the modulated laser is shown at 30 in
In this example, it will be assumed that the output of the laser is linearly polarized, and that the light entering absorption cell 24 at 42 must be circularly polarized to excite the relevant CPT transitions in the quantum absorber utilized in the absorption cell. Hence, the output of the laser is passed through a quarter waveplate 23 prior to being applied to absorption cell 24.
Absorption cell 24 contains a quantum absorber having two ground states that are separated by an energy difference corresponding to a frequency difference of W. Each of the ground states is connected to a common excited state by an appropriate frequency component. As will be explained in more detail below, transitions from one of the ground states to the common excited state are induced by photons in frequency component 32, and transitions from the other of the ground states to the common excited state are induced by photons in frequency component 33. In a quantum absorber, the absorption cell has a minimum in its absorption when the frequency difference of the CPT-generating frequency components 32 and 33, i.e., 2ν, is equal to W, provided both CPT-generating frequency components are present. Hence, by adjusting the microwave frequency, ν, to maximize the light transmitted through absorption cell 24, microwave source 27 will be precisely locked at a frequency of W/2.
The spectrum of the light transmitted through the absorption cell 24 is shown at 40 in
Refer now to
To simplify the following discussion, we assume that the applied electromagnetic field is tuned to induce the transitions to the excited states F′=2. The effect of the F′=1 energy states, i.e., the states 14, 15, and 16 can be ignored in the following discussion. The D1 energy levels of 87Rb exhibit two sets of transitions that can be utilized to generate CPT. The transitions shown at 41 and 42 couple the ground states shown at 7 and 3 to an excited state shown at 12. These transitions are excited by the light with right-handed circular polarization. A similar pair of transitions shown at 43 and 44 couple ground states shown at 3 and 7 to a second common state shown at 10. Transitions 43 and 44 are excited by the light with left-handed circular polarization. The right-handed circular polarization is orthogonal to the left-handed circular polarization. For the purposes of the present discussion, the energy differences between the various states will be written in terms of the corresponding of frequencies of electromagnetic radiation that induces transitions between these levels. The energy difference between states 3 and 7 is equal to hW, where h is the Planck constant. The energy difference between states 3 and 12 and states 3 and 10 can be written as h(ν0−W/2), where hν0 is the average of the energy difference between the state 12 and state 3 and the energy difference between the state 12 and state 7. Similarly, the energy difference between states 7 and 12 and states 7 and 10 can be written as h(ν0+W/2). To enhance CPT, the laser carrier frequency, νL, must be approximately equal to ν0. Methods for controlling the laser carrier to keep νL≈ν0 are known to the art, and hence, will not be discussed here.
If 87Rb is illuminated with light having energy at both (ν0−W/2) and (ν0+W/2) the transmission of this light through the material is greater than the case in which light of either frequency alone is utilized. Hence, if the laser shown in
The present invention is based on the observation that CPT exhibits dichroism (absorption dependence on the polarization states) and birefringence (refractive index dependence on the polarization states), especially for the frequency components in resonance with the transitions associated with the energy states related to the CPT. Thus the polarization states of the CPT-generating frequency components are altered when those frequency components pass through the quantum absorber while the polarization states for the AC-Stark-shift manipulating frequency components are not altered substantially if these frequency components are de-tuned from the transition frequencies in the quantum absorber. In the example discussed above with reference to
The manner in which the present invention provides its advantages will now be explained in more detail utilizing
Refer now to
The output of modulated laser 22 is linearly polarized as shown in
Upon passing through absorption cell 24, both the energy spectrum and polarization of the light will have changed. The energy spectrum at locations 93 and 94 is shown in
The light transmitted through absorption cell 24 is applied to a second quarter waveplate 83 that converts the polarization of the light such that the light in the AC Stark manipulating components can be preferentially separated form the light in the CPT-generating frequency components by linear polarization analyzer 84. The axis of waveplate 83 is set such that upon leaving the quarter waveplate 83 the first group of frequency components is, in general, elliptically polarized while the second group of frequency components is linearly polarized. The azimuth and ellipticity of the polarization state, as well as the intensity of the first group of frequency components depend on the detuning 2ν−W. The elliptical polarization state for the first group of frequency components can be decomposed into two orthogonal linear polarizations with an appropriate relative phase as shown in
The light leaving quarter waveplate 83 is applied to a linear polarization analyzer 84 that blocks light having a polarization in the direction of the second group of frequency components at point 94. This filter blocks the light in the second group of frequency components and the portion of the light in the first group of frequency components that is parallel to that direction, i.e., component 104 shown in
The spectrum of the light entering photodetector 28 at 95 is shown in
The above-described embodiments of the present invention assume that the CPT in the quantum absorber is induced by circularly polarized light and that the quantum absorber exhibits birefringence with respect to the circular polarization states. That is, the quantum absorber introduces a phase shift into light of one circular polarization relative to the other circular polarization. In addition, the quantum absorber exhibits dichroism with respect to the circular polarization states. That is, the absorption of one circular polarization is different from the other circular polarization. However, not all CPT transitions are induced by circularly polarized light. Some materials, for example, have CPT transitions that are excited by elliptically polarized light. In such cases, the polarization of laser light must be converted to the desired polarization. Upon passing through the quantum absorber, some of the light having a polarization that is the same as the original elliptical polarization light without carrying the CPT-information will be blocked from the photodetector by a properly designed polarization analyzer.
Refer now to
The above-described embodiments of the present invention have only discussed the adjustment of the modulation source frequency. However, in the preferred embodiment of the invention, the amplitude of the modulation signal is also adjusted to minimize the AC Stark shift in the CPT levels in the quantum absorber. At the correct modulation amplitude, the frequency at which the modulation source is locked is independent of the amplitude of the light signal from the laser. This amplitude can be determined experimentally when the reference signal generator is manufactured. Alternatively, a servo loop can adjust the modulation signal amplitude to minimize the errors resulting from the AC Stark shift. Since such servo systems are known in the art, they will not be discussed in detail here. The reader is referred to the U.S. patents discussed above for a more detailed explanation.
The quantum absorber discussed above can be any material that is in resonance with the applied electromagnetic field emitted by the electromagnetic source and that exhibits the CPT effect. For example, other alkali metals such as lithium, sodium, potassium, and cesium can also be utilized. In addition, suitable ions, molecules, or doped crystalline materials can be utilized.
The material utilized in the quantum absorber can be in the solid, liquid, or gaseous form. For example, the quantum absorber based on 87Rb discussed above preferably comprises rubidium in the vapor state.
The above-described embodiments of the present invention utilize a modulated laser as the source of electromagnetic radiation to induce CPT in the quantum absorber. However, other suitable electromagnetic radiation sources can be utilized.
The above embodiments of the present invention have been directed to frequency standards in which the goal is to produce a standard signal whose frequency is independent of environmental conditions. However, the present invention can also be utilized to construct a sensor that measures some physical quantity such as magnetic field strength. Consider a quantum absorber in which the CPT is based on two low energy states having an energy difference that depends on an external magnetic field that is applied to the absorber material. By measuring the modulation frequency at which the CPT is maximized, the strength of the magnetic field can be deduced.
For example, a magnetic field strength measuring apparatus can be constructed using transitions between other states of 87Rb. The energy levels in the ground states of 87Rb shift in response to an external magnetic field that is applied to the atom. State 3 and state 7 discussed above shift very little in the weak field, and hence, those states are well suited for constructing a frequency source. Refer now to
Refer again to
Alternatively, CPT between the three pairs of states (state 2 and state 6, state 3 and state 7, and state 4 and state 8 in
Similar sensors can be constructed to measure electric field strength or other environmental variables by choosing the suitable energy states in a suitable quantum absorber for CPT generation.
The above-described embodiments of the present invention utilize an electromagnetic radiation source in which the CPT-generating frequency components and the AC Stark shift manipulating frequency components have the same polarization. In addition, these embodiments assume that the polarization of the AC Stark shift manipulating frequency components does not change in passing through the quantum absorber. In the more general case, the polarization of the two CPT-generating frequency components may be different from each other as well as being different from the AC Stark shift manipulating frequency components. For example, the output of multiple lasers may be combined to provide the electromagnetic radiation signal having the CPT and AC Stark shift manipulating frequency components. One of the CPT-generating frequency components may come from one laser while the other CPT-generating frequency component may come from a different laser with different polarization. As noted above, the polarization of the AC Stark shift manipulating frequency components may be different from that of the CPT-generating frequency components. For example, the electromagnetic radiation source can include two lasers, one for generating the CPT-generating frequency components and one for generating the AC Stark shift manipulating frequency components. In addition, the polarization state of each AC Stark shift manipulating frequency component could be different from the other AC Stark shift manipulating frequency components. Finally, it should be noted that the AC Stark shift manipulating frequency components may undergo some change in polarization after passing through the quantum absorber.
The present invention depends only on the observation that the polarization of AC Stark shift manipulating frequency components will be distinguishable from the polarization of the CPT-generating frequency components after both sets of frequency components have passed through the quantum absorber. The polarization analyzer is set to preferentially attenuate the intensity of at least one of the AC Stark shift manipulating frequency components relative to the intensity of the CPT-generating frequency components. Ideally, all of the AC Stark shift manipulating frequency components would be suppressed; however, significant improvements in signal-to-noise ratio can be obtained if only a subset of AC Stark shift manipulating frequency components is so attenuated.
Consider the case in which the CPT-generating frequency components have different polarizations. The present invention does not need to detect both components. It is sufficient that one component is detected. Hence, as long as the polarization analyzer improves the ratio of the power in the CPT-generating frequency components to the AC Stark manipulating components, the present invention will provide an improvement over prior art systems.
Various modifications to the present invention will become apparent to those skilled in the art from the foregoing description and accompanying drawings. Accordingly, the present invention is to be limited solely by the scope of the following claims.
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