Method and system for synchronizing separated clocks

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.

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'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.

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. 1illustrates a particle path equalizer apparatus (PPEA)10, which in some embodiments can be used for, among other things, synchronizing distant clocks. The configuration illustrated inFIG. 1represents the initialization phase of the distant clock synchronization. The PPEA10includes a correlated particle emitter (CPE)12, a variable particle delay element14, and a particle receiver16. The CPE12emits at least two correlated particles18and20. The correlated particles18and20are 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 CPE12according to a reference clock13that is inertial with respect to the PPEA10. 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 CPE12according to the reference clock13. In some embodiments, the CPE12emits streams of correlated particles, and consequently, the correlated particles18and20are in particle streams22and24, respectively.

Conceptually, the reference clock13is an idealized clock that does not suffer from imperfections of hardware, i.e., the reference clock13keeps perfect or proper time. Time measured with respect to the reference clock13is referred to as coordinate time, (t), which is a global quantity, which is associated with the metric of space-time, gij, 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 particles18and20are both particles and waves, and the particle streams22and24are both streams of particles and beams of waves.

The particle stream22is directed to a first target26along a transmission path (T1)28. The first target26includes a particle reflector30, and during this initialization, the particle reflector30reflects the incident particle stream22. Upon reflection, the particle stream22travels along a reflection path (R1)32to the particle receiver16.

The particle stream24travels from the CPE12to a second target34along a second transmission path (T2)36. The second target34includes a particle reflector38, and during initialization, the particle stream24is reflected by the particle reflector38along a second reflection path (R2)40. In some embodiments, the particle reflectors30and38are optical devices such as corner cube reflectors or mirrors. It should be noted that in some embodiments, the particle reflectors30and38are not 100% reflective.

The transmission path36has three legs: (1) from the CPE12to the variable particle delay element14; (2) through the variable particle delay element14; and (3) from the variable particle delay element14to the second target34. Similarly, the reflection path (R2)40has three legs: (1) from the second target34to the variable particle delay element14; (2) through the variable particle delay element14; and (3) from the variable particle delay element14to the particle receiver16.

The particle receiver16receives particle streams22and24. In some embodiments, the particle receiver16measures the amount of correlation between received particles carried by the particle streams22and24. For example, in one embodiment, the particles18and20are 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 receiver16is 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 (T1+R1) and (T2+R2) are the same.

A controller42is in communication with the PPEA10via electrical connectors44and46. Electrical connector44carries electrical signals from the particle receiver16to the controller42. Using the signals from the particle receiver16, the controller42provides control signals to the variable particle delay element14via electrical connector46. The variable particle delay element14responds to the control signals to change, or maintain, the particle path through the variable particle delay element14, i.e., to change, or maintain, the time that it takes the particle20to traverse the variable particle delay element14. In some embodiments, the variable particle delay element14is 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 element14, the time to traverse the variable particle delay element14is approximately independent of direction. In other words, for a given configuration, the transmission lag through the variable particle delay element14is approximately the same as the reflection leg through the variable particle delay element14. Furthermore, it should be noted that in a preferred embodiment, the correlated particle emitter12and the particle receiver16are disposed such that they are approximately coincident. By having the correlated particle emitter12approximately coincident with the particle receiver14, the time of flight along the transmission paths (T1, T2)28and36is approximately equal to the time of flight along the reflection paths (R1, R2)32and40, respectively. Generally, the transmission paths (T1, T2)28and36are spatially much greater than the physical separation of the correlated particle emitter12and the particle receiver16, and consequently, for all practical purposes the particle receiver16and correlated particle emitter12appear to be coincident as viewed from the targets26and34.

In one embodiment, the components of the PPEA10are 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 controller42is 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. 2is a block diagram of the correlated particle emitter12for an embodiment that employs biphotons. The correlated particle emitter12includes a laser48, a parametric down converter50, and tuners52and54. The laser48pumps a laser beam56into the parametric down converter50. The parametric down converter50generates/creates biphotons (correlated or entangled photon pairs) from the photons in the laser beam56. 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 beam56are conserved, the parametric down converter50produces/creates a pair of correlated particles18and20from a single photon in the laser beam56. Consequently, the laser beam56is transformed into the particle streams (laser beams)22and24by the parametric down converter50.

The tuners52and54receive particle streams (laser beams)22and24, respectively. The tuner52directs particle stream (laser beam)22along transmission path (T1)28, and the tuner54directs particle stream (laser beam)24along transmission path (T2)36. The tuners52and54are comprised of mirrors and other optical devices known to those skilled in the art.

In some embodiments, the laser48is a continuous wave laser such as an argon-ion laser oscillating at 351.1 nm, and the parametric down converter50is 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. 3illustrates components of the particle receiver16when the particle receiver is an HOM interferometer. The particle receiver16includes a beam splitter58, photon detectors60and62, and coincidence analyzer64. The beam splitter58is adapted to have equal reflectance and transmittance so that either photon detector60or62is equally or likely to receive either one of the particles (photon)18or20. The photon detectors60and62are in communication with the coincidence analyzer64via communication links66and68, respectively. Each of the photon detectors60and62signals the coincidence analyzer64when they detect a particle.

The coincidence analyzer64determines the number of coincidences, i.e., the number of particles that are detected at the photon detectors60and62per unit time. When the sum of the transmission path28and reflection path32(T1+R1) approximately equals the sum of the transmission path36and reflection path40(T2+R2), then, for the case of biphotons, the particles18and20arrive at the particle receiver16approximately simultaneously and experience destructive interference. The coincidence analyzer64communicates the number of coincidences to the controller42via the electrical connector44.

FIG. 4is 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 minimum70which corresponds with the sum of the transmission path28and reflection path32(T1+R1) approximately equaling the sum of the transmission path36and the reflection path40(T2+R2). 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. 5illustrates an exemplary flow chart for steps taken to initialize synchronization of distal clocks. In step72, 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 step74, streams of correlated particles are transmitted along separate paths. Particles in one stream are transmitted along transmission path (T1)28and reflection path (R1)32, and particles in another stream are transmitted along transmission path (T2)36and reflection path (R2)40.

Next, in step76, 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 emitter12to the particle receiver16is substantially equivalent on the two complete paths (28,32) and (36,40).

FIG. 6illustrates exemplary steps that are taken during step76for correlated particles such as biphotons. In step78, streams of correlated particles are received at an interferometer. Next in step80, the number of coincidences, i.e., the number of simultaneous arrivals of biphotons, is determined.

Next, in step82, the number of coincidences is minimized. The controller42controls the variable path delay element14such that the variable path delay element14is configured to minimize the number of coincidences.

Clock Synchronization

Referring toFIG. 7, in some embodiments, the targets26and34are satellites, which are in communication with a satellite control center84. The satellite control center84includes the necessary software, hardware, and personnel for controlling the targets/satellites26and34and for communicating with the targets/satellites26and34over communication links86and88, respectively. The controller42signals the satellite control center84, via a communication link90, when the transmission and reflection paths (28,32) and (36,40) (SeeFIG. 1) have been substantially equalized. The satellite control center84then signals the targets/satellites26and34to commence with synchronizing their respective clocks92and94.

The correlated particle emitter12emits particle streams22and24, which in some embodiments are comprised of biphotons. The particle stream22travels along the transmission path (T1)28to the target/satellite26, and the particle stream24travels along the transmission path (T2)36to the target/satellite34. Responsive to the signal from the satellite control center84, the targets/satellites26and34begin to collect particle arrival data for particles carried by the particle streams22and24, respectively.

In the embodiment illustrated inFIG. 7, the particle reflectors30and38are not shown. The targets/satellites26and34adjust/move their respective particle reflectors30and38responsive to receiving a signal from the satellite control center84, thereby exposing particle detectors96and98, respectively, to the particle beams22and24. In other embodiments, the particle reflectors30and38are not 100% reflective, and in that case, the particle detectors96and98are partially exposed to the particle beams22and24without adjusting/moving the particle reflectors30and38. In some embodiments, the particle detectors96and98are photodetectors.

The particle detectors96and98detect the arrival of particles and record the arrival times of the particles with respect to the clocks92and94, respectively. Photon arrival time data at satellite26is given by a set of numbers {τj(92)}, where j=1, N, which is typically about 1 million data points, which are recorded in a particle arrival table100. The satellite34also records photon arrival time data in a particle arrival table (not shown), and the arrival times of photons at the satellite34are denoted by the set of number {τj(94)}, where j=1, N. Typically, the intensity of particle streams22and24are such that about 1 million data points are accumulated at the targets/satellites26and34within approximately one second or so, or fast enough such that mechanical imperfections in the clocks92and94can 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 clocks92and94appear 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 clock92, the “proper time” elapsed between the reception of the first particle (tl(92)) and the kthparticle (tk(92)) recorded in the particle arrival table100is given by: τk(92)+Δτ(92)=tk(92)−tl(92), where τk(92)is the time that the kthparticle arrived as measured by clock92, and Δτ(92)is the clock correaction that relates coordinate time (t) to “proper time” for clock92. Similarly, on the world line of clock94, the “proper time” elapsed between the reception of the first particle (tl(94)) and the kthparticle (tk(94)) recorded in the particle arrival table of target/satellite34is given by: τk(94)+Δτ(94)=tk(94)−tl(94), where τk(94)is the time that the kthparticle arrived as measured by clock94, and ττ(94)is the clock correaction that relates coordinate time (t) to “proper time” for clock94.

After a predetermined amount of time or a predetermined amount of data has been collected, the target/satellite26provides the target/satellite34with a particle arrival table100. The particle arrival table100includes the particle arrive time data102for target/satellite26. Typically, the particle arrival table100may include about 1,000,000 data points, i.e., arrival times. The particle arrival table100may be transmitted directly between targets/satellites26and34or through one or more intermediaries such as the satellite control center84.

Photons that are coincident at clock92and94are 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. 8is a block diagram of selected components of satellite34. In addition to the clock94and the detector98, satellite34includes a processor104, a memory106, and a receiver108, which are coupled to a bus110. The receiver94receives messages/signals from the satellite control center84and provides the processor104with the messages/signals. The receiver108also receives the particle arrival table100, which is provided to the processor104and stored in the memory106.

The memory106includes a particle arrival table112, which is a recordation of particle arrival times at the satellite34as determined by the detector98using clock94, and a clock synchronization module114. The processor104implements the clock synchronization module114using the particle arrival tables100and112to synchronize the clock94to the clock92. The clock synchronization module114includes the logic for calculating a correlation between the particle arrival times using the particle arrival tables100and112and for determining and applying an offset for clock94. In some embodiments, the clock synchronization module also includes the logic for controlling the particle reflector30.

FIG. 9is 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 step118, multiple streams of quantum mechanically correlated particles are created, and next in step120, the streams of quantum mechanically correlated particles are transmitted along transmission paths (T1)28and (T2)36.

Next in step122, the targets/satellites26and34receive the streams of correlated particles. The target/satellites26and34use their clocks92and94, respectively, to determine the arrival times of the particles.

Next in step124, the clock94is synchronized with the clock92using arrival times of particles at the target/satellite26.

FIG. 10further illustrates exemplary steps that are implemented during steps122and124. In step126, the target/satellites26and34record particle arrival times in their respective particle arrival tables100. Next in step128, the particle arrival table100of target/satellite26is provided to the target/satellite34.

Next in step130, the target/satellite34correlates the arrival times of the different particle streams using its particle arrival table (not shown) and the particle arrival time table100of the target/satellite26. The correlation function g(τ) is computed

g⁡(τ)=1N⁢∑i=1N⁢∑j=1N⁢δ⁡(τ-τj(92)+τi(94))
where N is the number of detected particles, τj(92)is the arrival time, as measured by clock92, of the jthparticle, τi(94)is the arrival time, as measured by clock94, of the ithparticle, and δ is the Dirac delta function.

Next, in step132, an offset (τ0) for clock94is determined. The offset is given by the maximum in the correlation function g(τ).

Next, in step134, the offset is applied to clock94. After applying the offset, clocks92and94are synchronized. It should be noted that the clocks92and94are 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 PPEA10.

It should be noted, that in the case where the particles18and20are biphotons, the clocks92and94are 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.