Abstract:
Methods and systems for synchronizing a first clock with a second clock, wherein the clocks are separated, are disclosed. A representative system, among others, includes a correlated particle emitter that emits a first particle stream and a second particle stream. Particles in the first particle streams are quantum mechanically correlated with particles in the second particle stream. The system also includes: a first target having the first clock and a first particle detector, and a second target having the second clock and a second particle detector. The first target uses the first clock and the first particle detector to determine arrival times of particles included in the first particle stream, and the second target uses the second clock and the second particle detector to determine arrival times of particles included in the first particle stream.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
   This application claims priority to copending U.S. provisional application entitled, “Method For Accurate Time Transfer, Clock Synchronization, And Navigation In Curved Space-Time,” having Ser. No. 60/499,411, filed 26 Aug., 2003, which is entirely incorporated herein by reference. 

   GOVERNMENT INTEREST 
   The invention described herein may be manufactured and used by or for the United States Government for governmental purposes without the payment of any royalties thereon. 
   BACKGROUND 
   1. Technical Field 
   The present invention is generally related to the synchronization of clocks that are separated. 
   2. Description of the Related Art 
   High-accuracy synchronization of clocks plays an important role in fundamental physics and in a wide range of applications such as communications, message encryption, navigation, geolocation and homeland security. A classical method of time synchronization of spatially separated clocks is Eddington slow clock transport. In this approach, two co-located clocks are initially synchronized, and then one of the clocks is slowly transported to another location to synchronize with a distant clock, i.e., a geographically separated clock. For most technological applications, this method is not practical because it requires transport of hardware, i.e., the clock, as well as conflicting requirements: on the one hand, clock transport must be slow to reduce the relativistic effect of time dilation, but on the other hand, the transport must be fast enough so that significant time differences do not accrue from unavoidable timing errors due to the limited frequency stability of the transported clock&#39;s mechanism or due to gravitational potential differences along the path of the transported clock. 
   Today, in practical applications, a satellite system, such as the Global Positioning System (GPS), is used for synchronizing two spatially separated clocks. GPS is a satellite system in which signals are sent from satellite-to-ground and from ground-to-satellite to synchronize the satellite clocks with a master clock on the Earth. The time-synchronization accuracy provided by a GPS receiver is on the order of 20 nanoseconds (ns). However, there are applications, such as coherent detection of high-frequency electromagnetic signals, where time synchronization is required to an accuracy that cannot be provided by GPS. Therefore, there exists a need for synchronizing spatially separated clocks to an accuracy better than the nanosecond range 
   SUMMARY 
   Systems and methods for synchronizing a first clock with a second clock, wherein the clocks are separated, are disclosed. A representative system, among others, includes a correlated particle emitter that emits a first particle stream and a second particle stream. Particles in the first particle stream are quantum mechanically correlated with particles in the second particle stream. The system also includes: a first target having the first clock and a first particle detector, and a second target having the second clock and a second particle detector. The first target uses the first clock and the first particle detector to determine arrival times of particles included in the first particle stream, and the second target uses the second clock and the second particle detector to determine arrival times of particles included in the second particle stream. 
   An embodiment of a method can be broadly summarized by the following steps: transmitting along a first particle path a first stream of particles to a target having the first clock; transmitting along a second particle path a second stream of particles to a second target having the second clock; determining an offset for the first clock based upon arrival times of particles in the first stream of particles at the first target and upon arrival times of particles in the second stream of particles at the second target; and applying the offset to the first clock. 
   Other systems, methods, features, and/or advantages will be or may become apparent to one with skill in the art upon examination of the following drawings and detailed description. It is intended that all such additional systems, methods, features, and/or advantages be included within this description and be protected by the accompanying claims. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The components in the drawings are not necessarily to scale. Moreover, in the drawings, like reference numerals designate corresponding parts throughout the several views. 
       FIG. 1  is a block diagram of an embodiment of a particle path equalizer apparatus (PPEA) and two separated clocks. 
       FIG. 2  is a block diagram of an embodiment of a correlated particle emitter. 
       FIG. 3  is a block diagram of an embodiment of a particle receiver. 
       FIG. 4  is a plot of number of coincidences versus particle delay. 
       FIG. 5  is an exemplary flow chart of a method for creating substantially equivalent particle paths. 
       FIG. 6  is an exemplary flow chart of a method for creating substantially equivalent particle paths using biphotons. 
       FIG. 7  is a block diagram of an embodiment of a particle path equalizer apparatus (PPEA) synchronizing clocks on two satellites. 
       FIG. 8  is a block diagram of an embodiment of selected components of a satellite. 
       FIG. 9  is an exemplary flow chart of a method for synchronizing two separated clocks. 
       FIG. 10  is an exemplary flow chart of a method for synchronizing two separated clocks using particle arrival tables. 
   

   DETAILED DESCRIPTION 
   It should be emphasized that the above-described embodiments are merely possible examples of implementations. Many variations and modifications may be made to the above-described embodiments. All such modifications and variations are intended to be included herein within the scope of this disclosure and the present invention and protected by the following claims. 
     FIG. 1  illustrates a particle path equalizer apparatus (PPEA)  10 , which in some embodiments can be used for, among other things, synchronizing distant clocks. The configuration illustrated in  FIG. 1  represents the initialization phase of the distant clock synchronization. The PPEA  10  includes a correlated particle emitter (CPE)  12 , a variable particle delay element  14 , and a particle receiver  16 . The CPE  12  emits at least two correlated particles  18  and  20 . The correlated particles  18  and  20  are quantum mechanically correlated such that there is a known, or a quantum mechanically predictable, relationship between their respective emission times or creation times. For the purposes of this disclosure the emission time for a particle is defined as the time at which the particle is emitted from the CPE  12  according to a reference clock  13  that is inertial with respect to the PPEA  10 . For the purposes of this disclosure the creation time for a particle is defined as the time at which the particle is created in the CPE  12  according to the reference clock  13 . In some embodiments, the CPE  12  emits streams of correlated particles, and consequently, the correlated particles  18  and  20  are in particle streams  22  and  24 , respectively. 
   Conceptually, the reference clock  13  is an idealized clock that does not suffer from imperfections of hardware, i.e., the reference clock  13  keeps perfect or proper time. Time measured with respect to the reference clock  13  is referred to as coordinate time, (t), which is a global quantity, which is associated with the metric of space-time, g ij , and enters into the definition of the system of 4-dimensional space-time coordinates. 
   Those skilled in the art understand the wave particle duality principle elucidated by DeBroglie. Consequently, the correlated particles  18  and  20  are both particles and waves, and the particle streams  22  and  24  are both streams of particles and beams of waves. 
   The particle stream  22  is directed to a first target  26  along a transmission path (T 1 )  28 . The first target  26  includes a particle reflector  30 , and during this initialization, the particle reflector  30  reflects the incident particle stream  22 . Upon reflection, the particle stream  22  travels along a reflection path (R 1 )  32  to the particle receiver  16 . 
   The particle stream  24  travels from the CPE  12  to a second target  34  along a second transmission path (T 2 )  36 . The second target  34  includes a particle reflector  38 , and during initialization, the particle stream  24  is reflected by the particle reflector  38  along a second reflection path (R 2 )  40 . In some embodiments, the particle reflectors  30  and  38  are optical devices such as corner cube reflectors or mirrors. It should be noted that in some embodiments, the particle reflectors  30  and  38  are not 100% reflective. 
   The transmission path  36  has three legs: (1) from the CPE  12  to the variable particle delay element  14 ; (2) through the variable particle delay element  14 ; and (3) from the variable particle delay element  14  to the second target  34 . Similarly, the reflection path (R 2 )  40  has three legs: (1) from the second target  34  to the variable particle delay element  14 ; (2) through the variable particle delay element  14 ; and (3) from the variable particle delay element  14  to the particle receiver  16 . 
   The particle receiver  16  receives particle streams  22  and  24 . In some embodiments, the particle receiver  16  measures the amount of correlation between received particles carried by the particle streams  22  and  24 . For example, in one embodiment, the particles  18  and  20  are biphotons (correlated or entangled photon pairs, such as are produced by the process of spontaneous parametric down-conversion (SPDC) when a non-linear crystal is pumped by a laser) and the particle receiver  16  is a Hong-Ou-Mandel (HOM) interferometer, which measures the amount of interference (i.e., two-photon coincident counting rate) between correlated biphotons. The destructive interference between correlated biphotons is a maximum (i.e., minimum in the two-photon coincident counting rate) when the optical paths (T 1 +R 1 ) and (T 2 +R 2 ) are the same. 
   A controller  42  is in communication with the PPEA  10  via electrical connectors  44  and  46 . Electrical connector  44  carries electrical signals from the particle receiver  16  to the controller  42 . Using the signals from the particle receiver  16 , the controller  42  provides control signals to the variable particle delay element  14  via electrical connector  46 . The variable particle delay element  14  responds to the control signals to change, or maintain, the particle path through the variable particle delay element  14 , i.e., to change, or maintain, the time that it takes the particle  20  to traverse the variable particle delay element  14 . In some embodiments, the variable particle delay element  14  is adapted to vary its index of refraction, thereby providing variable delay for light waves (photons). 
   It should be noted that for a given configuration of the variable particle delay element  14 , the time to traverse the variable particle delay element  14  is approximately independent of direction. In other words, for a given configuration, the transmission lag through the variable particle delay element  14  is approximately the same as the reflection leg through the variable particle delay element  14 . Furthermore, it should be noted that in a preferred embodiment, the correlated particle emitter  12  and the particle receiver  16  are disposed such that they are approximately coincident. By having the correlated particle emitter  12  approximately coincident with the particle receiver  14 , the time of flight along the transmission paths (T 1 , T 2 )  28  and  36  is approximately equal to the time of flight along the reflection paths (R 1 , R 2 )  32  and  40 , respectively. Generally, the transmission paths (T 1 , T 2 )  28  and  36  are spatially much greater than the physical separation of the correlated particle emitter  12  and the particle receiver  16 , and consequently, for all practical purposes the particle receiver  16  and correlated particle emitter  12  appear to be coincident as viewed from the targets  26  and  34 . 
   In one embodiment, the components of the PPEA  10  are disposed on a microchip, which includes the necessary circuitry for providing communication paths between the components. In other components, the components are separate modules. Those skilled in the art are familiar with networking of the components such that power and signals are provided to the necessary components. 
   Generally, the controller  42  is a processing device that can include any custom made or commercially available processor, a central processing unit (CPU) or an auxiliary processor among several processors associated with the computer system, a semiconductor based microprocessor (in the form of a microchip), a macroprocessor, one or more application specific integrated circuits (ASICs), a plurality of suitably configured digital logic gates, and other well known electrical configurations comprising discrete elements both individually and in various combinations to coordinate the overall operation of the computing system. 
     FIG. 2  is a block diagram of the correlated particle emitter  12  for an embodiment that employs biphotons. The correlated particle emitter  12  includes a laser  48 , a parametric down converter  50 , and tuners  52  and  54 . The laser  48  pumps a laser beam  56  into the parametric down converter  50 . The parametric down converter  50  generates/creates biphotons (correlated or entangled photon pairs) from the photons in the laser beam  56 . Those skilled in the art know that biphotons are a pair of photons that are created simultaneously from a single photon. Because both energy and momentum of the incident laser beam  56  are conserved, the parametric down converter  50  produces/creates a pair of correlated particles  18  and  20  from a single photon in the laser beam  56 . Consequently, the laser beam  56  is transformed into the particle streams (laser beams)  22  and  24  by the parametric down converter  50 . 
   The tuners  52  and  54  receive particle streams (laser beams)  22  and  24 , respectively. The tuner  52  directs particle stream (laser beam)  22  along transmission path (T 1 )  28 , and the tuner  54  directs particle stream (laser beam)  24  along transmission path (T 2 )  36 . The tuners  52  and  54  are comprised of mirrors and other optical devices known to those skilled in the art. 
   In some embodiments, the laser  48  is a continuous wave laser such as an argon-ion laser oscillating at 351.1 nm, and the parametric down converter  50  is a crystal that lacks inversion symmetry. Examples of crystals used in parametric down conversion are a barium beta borate or a potassium dihydrogen phosphate crystal. 
     FIG. 3  illustrates components of the particle receiver  16  when the particle receiver is an HOM interferometer. The particle receiver  16  includes a beam splitter  58 , photon detectors  60  and  62 , and coincidence analyzer  64 . The beam splitter  58  is adapted to have equal reflectance and transmittance so that either photon detector  60  or  62  is equally or likely to receive either one of the particles (photon)  18  or  20 . The photon detectors  60  and  62  are in communication with the coincidence analyzer  64  via communication links  66  and  68 , respectively. Each of the photon detectors  60  and  62  signals the coincidence analyzer  64  when they detect a particle. 
   The coincidence analyzer  64  determines the number of coincidences, i.e., the number of particles that are detected at the photon detectors  60  and  62  per unit time. When the sum of the transmission path  28  and reflection path  32  (T 1 +R 1 ) approximately equals the sum of the transmission path  36  and reflection path  40  (T 2 +R 2 ), then, for the case of biphotons, the particles  18  and  20  arrive at the particle receiver  16  approximately simultaneously and experience destructive interference. The coincidence analyzer  64  communicates the number of coincidences to the controller  42  via the electrical connector  44 . 
     FIG. 4  is a plot of the number of coincidences, i.e., the number of photons detected, as a function of variable delay. The number of coincidences exhibits a minimum  70  which corresponds with the sum of the transmission path  28  and reflection path  32  (T 1 +R 1 ) approximately equaling the sum of the transmission path  36  and the reflection path  40  (T 2 +R 2 ). In some embodiments of the system, a maximum in the two-photon coincidence counting rates can be observed and used for synchronization of the clocks. 
     FIG. 5  illustrates an exemplary flow chart for steps taken to initialize synchronization of distal clocks. In step  72 , multiple streams of quantum mechanically correlated particles are created. A given particle in one stream has a quantum mechanically correlated particle in another stream. The correlation between two or more particles enables measurements, or observables, on and between the correlated particles such as interference. Although, one embodiment is described in terms of employing biphotons, this is done merely for exemplary purposes, and in some embodiments, different correlated particles could be employed. Next, in step  74 , streams of correlated particles are transmitted along separate paths. Particles in one stream are transmitted along transmission path (T 1 )  28  and reflection path (R 1 )  32 , and particles in another stream are transmitted along transmission path (T 2 )  36  and reflection path (R 2 )  40 . 
   Next, in step  76 , the particle path of one of the streams is adjusted such that the paths are substantially equivalent. It should be noted that the two transmission and reflective paths ( 28 ,  32 ) and ( 36 ,  40 ) are substantially temporally equivalent, i.e., the time of flight from the correlated particle emitter  12  to the particle receiver  16  is substantially equivalent on the two complete paths ( 28 ,  32 ) and ( 36 ,  40 ). 
     FIG. 6  illustrates exemplary steps that are taken during step  76  for correlated particles such as biphotons. In step  78 , streams of correlated particles are received at an interferometer. Next in step  80 , the number of coincidences, i.e., the number of simultaneous arrivals of biphotons, is determined. 
   Next, in step  82 , the number of coincidences is minimized. The controller  42  controls the variable path delay element  14  such that the variable path delay element  14  is configured to minimize the number of coincidences. 
   Clock Synchronization 
   Referring to  FIG. 7 , in some embodiments, the targets  26  and  34  are satellites, which are in communication with a satellite control center  84 . The satellite control center  84  includes the necessary software, hardware, and personnel for controlling the targets/satellites  26  and  34  and for communicating with the targets/satellites  26  and  34  over communication links  86  and  88 , respectively. The controller  42  signals the satellite control center  84 , via a communication link  90 , when the transmission and reflection paths ( 28 ,  32 ) and ( 36 ,  40 ) (See  FIG. 1 ) have been substantially equalized. The satellite control center  84  then signals the targets/satellites  26  and  34  to commence with synchronizing their respective clocks  92  and  94 . 
   The correlated particle emitter  12  emits particle streams  22  and  24 , which in some embodiments are comprised of biphotons. The particle stream  22  travels along the transmission path (T 1 )  28  to the target/satellite  26 , and the particle stream  24  travels along the transmission path (T 2 )  36  to the target/satellite  34 . Responsive to the signal from the satellite control center  84 , the targets/satellites  26  and  34  begin to collect particle arrival data for particles carried by the particle streams  22  and  24 , respectively. 
   In the embodiment illustrated in  FIG. 7 , the particle reflectors  30  and  38  are not shown. The targets/satellites  26  and  34  adjust/move their respective particle reflectors  30  and  38  responsive to receiving a signal from the satellite control center  84 , thereby exposing particle detectors  96  and  98 , respectively, to the particle beams  22  and  24 . In other embodiments, the particle reflectors  30  and  38  are not 100% reflective, and in that case, the particle detectors  96  and  98  are partially exposed to the particle beams  22  and  24  without adjusting/moving the particle reflectors  30  and  38 . In some embodiments, the particle detectors  96  and  98  are photodetectors. 
   The particle detectors  96  and  98  detect the arrival of particles and record the arrival times of the particles with respect to the clocks  92  and  94 , respectively. Photon arrival time data at satellite  26  is given by a set of numbers {τ j   (92) }, where j=1, N, which is typically about 1 million data points, which are recorded in a particle arrival table  100 . The satellite  34  also records photon arrival time data in a particle arrival table (not shown), and the arrival times of photons at the satellite  34  are denoted by the set of number {τ j   (94) }, where j=1, N. Typically, the intensity of particle streams  22  and  24  are such that about 1 million data points are accumulated at the targets/satellites  26  and  34  within approximately one second or so, or fast enough such that mechanical imperfections in the clocks  92  and  94  can be ignored, or that motion of the two clocks can be ignored, or, a separate correaction can be made for clock motion. The data accumulation occurs fast enough that the clocks  92  and  94  appear to be ideal clocks having “proper time”, or alternatively, that a clock correaction can be applied to the time kept by the real hardware clock to make it effectively keep proper time to the needed accuracy. On the world line of clock  92 , the “proper time” elapsed between the reception of the first particle (t l   (92) ) and the k th  particle (t k   (92) ) recorded in the particle arrival table  100  is given by: τ k   (92) +Δτ (92) =t k   (92) −t l   (92) , where τ k   (92)  is the time that the k th  particle arrived as measured by clock  92 , and Δτ (92)  is the clock correaction that relates coordinate time (t) to “proper time” for clock  92 . Similarly, on the world line of clock  94 , the “proper time” elapsed between the reception of the first particle (t l   (94) ) and the k th  particle (t k   (94) ) recorded in the particle arrival table of target/satellite  34  is given by: τ k   (94) +Δτ (94) =t k   (94) −t l   (94) , where τ k   (94)  is the time that the k th  particle arrived as measured by clock  94 , and ττ (94)  is the clock correaction that relates coordinate time (t) to “proper time” for clock  94 . 
   After a predetermined amount of time or a predetermined amount of data has been collected, the target/satellite  26  provides the target/satellite  34  with a particle arrival table  100 . The particle arrival table  100  includes the particle arrive time data  102  for target/satellite  26 . Typically, the particle arrival table  100  may include about 1,000,000 data points, i.e., arrival times. The particle arrival table  100  may be transmitted directly between targets/satellites  26  and  34  or through one or more intermediaries such as the satellite control center  84 . 
   Photons that are coincident at clock  92  and  94  are defined to be those that are simultaneous in the inertial system of space-time coordinates which is defined by the frame of reference of the particle (biphoton) emitter. 
     FIG. 8  is a block diagram of selected components of satellite  34 . In addition to the clock  94  and the detector  98 , satellite  34  includes a processor  104 , a memory  106 , and a receiver  108 , which are coupled to a bus  110 . The receiver  94  receives messages/signals from the satellite control center  84  and provides the processor  104  with the messages/signals. The receiver  108  also receives the particle arrival table  100 , which is provided to the processor  104  and stored in the memory  106 . 
   The memory  106  includes a particle arrival table  112 , which is a recordation of particle arrival times at the satellite  34  as determined by the detector  98  using clock  94 , and a clock synchronization module  114 . The processor  104  implements the clock synchronization module  114  using the particle arrival tables  100  and  112  to synchronize the clock  94  to the clock  92 . The clock synchronization module  114  includes the logic for calculating a correlation between the particle arrival times using the particle arrival tables  100  and  112  and for determining and applying an offset for clock  94 . In some embodiments, the clock synchronization module also includes the logic for controlling the particle reflector  30 . 
     FIG. 9  is a flow chart of exemplary steps taken in clock synchronization. For the sake of clarity this description illustrates synchronizing two clocks, but in some embodiments, more than two clocks are synchronized. Those skilled in the art would know how to generalize the steps for more than two clocks. 
   In step  118 , multiple streams of quantum mechanically correlated particles are created, and next in step  120 , the streams of quantum mechanically correlated particles are transmitted along transmission paths (T 1 )  28  and (T 2 )  36 . 
   Next in step  122 , the targets/satellites  26  and  34  receive the streams of correlated particles. The target/satellites  26  and  34  use their clocks  92  and  94 , respectively, to determine the arrival times of the particles. 
   Next in step  124 , the clock  94  is synchronized with the clock  92  using arrival times of particles at the target/satellite  26 . 
     FIG. 10  further illustrates exemplary steps that are implemented during steps  122  and  124 . In step  126 , the target/satellites  26  and  34  record particle arrival times in their respective particle arrival tables  100 . Next in step  128 , the particle arrival table  100  of target/satellite  26  is provided to the target/satellite  34 . 
   Next in step  130 , the target/satellite  34  correlates the arrival times of the different particle streams using its particle arrival table (not shown) and the particle arrival time table  100  of the target/satellite  26 . The correlation function g(τ) is computed 
             g   ⁡     (   τ   )       =       1   N     ⁢       ∑     i   =   1     N     ⁢       ∑     j   =   1     N     ⁢     δ   ⁡     (     τ   -     τ   j     (   92   )       +     τ   i     (   94   )         )                   
where N is the number of detected particles, τ j   (92)  is the arrival time, as measured by clock  92 , of the j th  particle, τ i   (94)  is the arrival time, as measured by clock  94 , of the i th  particle, and δ is the Dirac delta function.
 
   Next, in step  132 , an offset (τ 0 ) for clock  94  is determined. The offset is given by the maximum in the correlation function g(τ). 
   Next, in step  134 , the offset is applied to clock  94 . After applying the offset, clocks  92  and  94  are synchronized. It should be noted that the clocks  92  and  94  are synchronized with respect to each other, but they are not necessarily synchronized with respect to a reference clock (not shown) that is inertial with respect to the PPEA  10 . 
   It should be noted, that in the case where the particles  18  and  20  are biphotons, the clocks  92  and  94  are synchronized with an accuracy in the range of picoseconds to femtoseconds, depending on the particular design of system components. 
   It should be emphasized that the above-described embodiments are merely possible examples of implementations. Many variations and modifications may be made to the above-described embodiments. All such modifications and variations are intended to be included herein within the scope of this disclosure and the present invention and protected by the following claims.