FIELD OF THE INVENTION

[001] The present invention generally relates to atomic clocks. More particularly, the present invention relates to apparatuses, systems and methods for atomic clocks with a combination of different atomic species.

BACKGROUND OF THE INVENTION

[002] Atomic clocks provide the highest accuracy for time and frequency standards, and are used as primary standards for time distribution services (such as those on the Internet) to control the frequencies of communication signals, in surveying, in navigation (such as GPS) and to make precise measurements of geological and relativistic phenomena.

[003] Atomic clocks include three main parts: an electromagnetic oscillator, an atomic reference system to which the oscillator locks, in particular, a narrow atomic transition of a single atomic species having a specific characteristic frequency, and a frequency counter which translates a count of oscillator periods to a time unit. The atomic reference is usually carefully chosen to be isolated and protected in order to minimize or eliminate the influence of variations in environmental conditions on the characteristic frequency accuracy of the atomic reference.

[004] Environmental conditions that influence the characteristic frequency of the atomic reference fall into two categories: one category features relativistic effects, such as second-order Doppler shifts and gravitational red-shifts - these effects can be countered by insuring that the reference atoms are in an inertial reference frame (e.g., zero gravity, free fall, non-rotating, etc.). The other category involves different physical phenomena in the environment that affect the characteristic frequencies of the atomic reference, such as magnetic fields, blackbody radiation, and so forth. This source of error is typically reduced by isolating and protecting the atomic reference from such influence (e.g., minimizing background electromagnetic fields, providing shielding, and so forth). Despite the best efforts at isolating and protecting the atomic reference from environmental factors, some influence typically remains. It is therefore desirable to reduce the influence of environmental factors on the atomic reference of atomic clocks.

SUMMARY OF THE INVENTION

[005] To overcome the limitations of current atomic clocks, which rely on a single atom species for a reference, embodiments of the present invention improve the accuracy and stability of an atomic clock by reducing the susceptibility of the atomic reference transition's characteristic frequency to changes in environmental electromagnetic conditions, via a quantum superposition of multiple different atomic species to compensate for the environmental variations.

[006] According to some embodiments of the invention, a pair of complementary atomic species is placed in a quantum superposition for use in an atomic clock, wherein the complementary superposed species have mutually-opposite susceptibilities to a particular environmental condition. While each of the respective species exhibits its own characteristic frequency in response to changes in the environmental condition, the complementary nature of the pair of species is such that their quantum superposition may exhibits a characteristic frequency which is the sum of their individual characteristic frequencies, such that the quantum superposition is relatively insensitive to those changes. In some embodiments of the invention, this concept is expanded to include a superposition of more than two species having mutually-complementary properties. Where more than two species are superposed, the species collectively complement one another so that the superposition of the multiple species has a reduced susceptibility to changes in the environmental condition. In particular, an atomic clock apparatus with a quantum superposition of two or more complementary species may be provided for obtaining improved frequency stability by summing the individual frequencies of the superposed complementary species.

[007] In some embodiments of the invention, multiple atoms of different species are superposed such that they are in an entangled quantum state, that is, a quantum superposition where their individual states are no longer independent of one another. It is noted that quantum coherence times may be increased by improving the coherence properties of the superposition. In some embodiments, the use of a decoherence-free subspace (e.g., insensitive to magnetic fields) prolongs the coherence time of the superposition. In some embodiment that include entangled superposition of different states, the total combined susceptibility of the entangled superposition is very small, resulting in a significant improvement in coherence. In some embodiments, blackbody radiation shift is reduced by having two different atomic transitions for the superposed atomic species, and using a frequency comb to generate a synthetic frequency (of the entangled superposition) that is substantially immune to the blackbody radiation shift.

[008] A maximally-entangled multi-atom state can in principle surpass the resolution attainable with uncorrected atoms (due to standard quantum limit) and be able to reach the Heisenberg limit. However, in practice the limit is given by the coherence time of the measurement. Therefore, according to some embodiment of the present invention there is provided an atomic clock apparatus including: (a) an atomic reference having a characteristic frequency, and (b) a local oscillator locked to the characteristic frequency of the atomic reference; wherein: (c) the atomic reference includes a quantum superposition of a plurality of different atomic species; (d) the characteristic frequency of the atomic reference is a characteristic frequency of the quantum superposition; and wherein (c) the different atomic species are pre-selected to have respective susceptibilities to an environmental condition which collectively complement one another, such that the characteristic frequency of the quantum superposition of the plurality of different atomic species has a reduced susceptibility to changes in the environmental condition.

[009] In addition, according to some embodiment of the present invention there is also provided a method for operating an atomic clock apparatus, the atomic clock apparatus including a plurality of different atomic species as an atomic reference and including a local oscillator, the method including: (a) initializing each of the atomic species in the plurality of different atomic species; (b) combining the plurality of different atomic species in a quantum superposition; (c) interrogating the atomic species at a reference frequency that is characteristic of the quantum superposition of the plurality of different atomic species; and (d) locking the local oscillator to the reference frequency. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] The subject matter disclosed may best be understood by reference to the following detailed description when read with the accompanying drawings in which:

[0011] Fig. 1 schematically illustrates an atomic combination clock, according to some embodiments of the present invention;

[0012] Fig. 2 shows a flowchart of an operational method for atomic combination clock having an entangled superposition of two different species, according to some embodiments of the present invention; and

[0013] Fig. 3 shows a flowchart for a method of operating an atomic combination clock, according to some embodiments of the present invention.

[0014] For simplicity and clarity of illustration, elements shown in the figures are not necessarily drawn to scale, and the dimensions of some elements may be exaggerated relative to other elements. In addition, reference numerals may be repeated among the figures to indicate corresponding or analogous elements.

DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION

[0015] In the following description, numerous specific details are set forth in order to provide a thorough understanding of the invention. However, it will be understood by those skilled in the art that the present invention may be practiced without these specific details as well as with other specific details. In the descriptions and drawings, well- known methods, procedures, and components are described in simple terms so as not to obscure the present invention.

[0016] For purposes of illustration, certain non-limiting embodiments presented herein are disclosed in the context of a quantum superposition of atomic ion species. It is understood that the present invention is not limited to quantum superposition of ions, but the principles thereof are applicable to quantum superposition of atomic species in other states, including, but not limited to: atoms in optical lattices or other solid-state bulk material, free atoms, including neutral atoms, such as atoms in the gaseous state, in atom beams, or in atomic fountains, and atomic species in neutral molecules or in molecular ions. [0017] In addition, the embodiments of the present invention are not limited to the use of optical transitions only. Various embodiments of the invention combine optical transitions with microwave hyperfine transitions in an entangled quantum superposition. The resulting effective characteristic clock frequency may be close to that of the optical component, but the magnetic susceptibility of the superposition can be controlled, especially when working at a high magnetic field in the Paschen-Back regime. In this regime the effective g-factor of the hyperfine transition can be smoothly tuned to null the first order magnetic susceptibility of the superposition.

[0018] Furthermore, it is noted that the present invention is not limited to the use of entangled states only. In various embodiments of the invention, non-entangled superposed states are used which overlap the desired entangled state. The advantage being reduced technical complexity, because an entangling operation is not needed. A parity measurement yields the same information, but at lower parity contrast and therefore a lower signal-to-noise ratio.

[0019] In some non-limiting embodiments of the present invention, quantum superposed atomic species may be ions of different elements. These embodiments employ generalized Ramsey spectroscopy similar to the case of identical ions in a maximally-entangled state. For instance, an 'N' multi-species atomic ensemble may be prepared for a quantum superposition of two states Ψ = -i= (| G) + e' ⁿ '| E)) ,

^■ V 2

where G = are product states of only the ground state (g) and

excited state (e) manifolds. The excited states (e) are assumed to be relatively long-lived and are optically separated from their ground state (g) counterparts, such that each state i has a characteristic frequency C0i which contributes to a total clock characteristic frequency Ω, where Ω = ω _ί .

[0020] Reference is now made to Fig. 1, which schematically illustrates an atomic combination clock 100, according to some embodiments of the invention. A quadrupole ion trap 101 spatially confines ions of two different atomic species, respectively represented as an A ⁺ ion 102 and a B ⁺ ion 103.

[0021] For an entangling operation, a first laser 104, denoted as "Laser A", may be tuned by an optical frequency comb 108 to emit a blue sideband pulse 105, and a second laser 106, denoted as "Laser B", may be tuned by the optical frequency comb 108 to emit a red sideband pulse 107. In some embodiments, the lasers may be tuned to the respective atomic resonance transitions (e.g., laser B 107 may be tuned to the atomic resonance transition of B ⁺ ions 103). The ions 102 and 103 may thus be entangled in an entangled state 110.

[0022] According to some embodiments, operation of the atomic combination clock 100 may be controlled by a controller 120 connected to a detector 130, for instance detector 130 to detect the entangled state 110. The controller 120 may also be operably connected to a local oscillator 140, which may be locked to the atomic reference characteristic frequency of the entangled state 110 of ions 102 and 103. The local oscillator 140 may therefore output a corresponding (stable) clock time 150 by translating counts of oscillator periods to time units.

[0023] It should be noted that while two different atomic species are sometimes described herein (represented as an A ⁺ ion 102 and a B ⁺ ion 103), multiple atomic species (more than two) may be entangled in a similar way. For generalized multiple atomic species, a plurality of lasers may be provided, wherein the lasers are respectively corresponding to each of the plurality of atomic species. In some embodiments, the local oscillator 140 may be configured to supply multiple local frequencies, such as multiple frequencies required for multiple atomic species.

[0024] According to some embodiments, after an interrogation time t = τ the phase between the quantum superposition of the entangled state 110 and the local oscillator 140 may be obtained by a global π/2 pulse followed by state detection (e.g., by detector 130) and parity analysis. When compared to the case of identical ions, the use of multiple species increases the complexity due to the need of having a set of lasers, including narrow-linewidth lasers, for each ion species. On the other hand, some technical aspects such as single-addressing and detection are simplified because of the available extra resources (e.g., of controller 120).

[0025] It should be noted that while ions are described above (e.g., ions 120 and 103) the atomic species may be selected from the group consisting of neutral atoms, elemental ions, neutral molecules, and molecular ions. [0026] Reference is now made to Fig. 2, which illustrates a flowchart for an operating sequence for atomic combination clock with a two species example, according to some embodiments of the invention. In some embodiments, the steps of the operating sequence may be performed and/or coordinated under the direction of an automated component in atomic combination clock, such as controller 120 shown in Fig. 1.

[0027] For an atomic combination clock (such as clock 100 shown in Fig. 1) with a two species example, the sequence illustrated in Fig. 2 begins with A ⁺ ion 102 and B ⁺ ion 103 both in their electronic ground states, a state | S ^A ^ 201 and a statej S ^e 202 respectively. The ions 102, 103 may also be in a normal mode of motion | 0 ^ 203 having a secular frequency .

[0028] In an initialization step 210 for A ⁺ ions 102, a π/2 blue sideband (BSB) pulse 213 (e.g., such as blue sideband pulse 105 shown in Fig. 1) may be applied to the A ⁺ ions 102, so that the internal state of A ⁺ ions 102 may be entangled 212 with the motion of the two-ion ensemble (such as entangled state 110 shown in Fig. 1). In a further initialization step 211 for B ⁺ ions 103, a π red sideband (RSB) pulse 214 (e.g., such as red sideband pulse 107 shown in Fig. 1) may be applied to B ⁺ ion 103, to entangle 212 a two-ion internal state 215 while disentangling the ions' motion. The two-ion internal state 215 may be described as: \ S ^A S ^B ) + \ D ^A D ^B ) .

[0029] In a rotating frame (e.g., due to the entanglement 212) with respect to atomic transitions with characteristic frequencies COA and ο¾, the resulting state may be:

\ S ^A )\ S ^A )\ S ^B )\ 0) ₊ \ D ^A )\ D ^B )\ I)) (1)

> -^(| s ^A )| S ^B ) + I D ^A )\ D ^B )\ 0)) where </> _tot = φ ₀ + (δ _Α + _B )t _int with 5A,B as the detuning of the two lasers 104, 106 from their corresponding atomic transitions, and φο is an arbitrary constant phase for zero interrogation time (e.g., the result of the pulses' times, light shift, etc.). The two-ion entangled state 215 may acquire a phase which is the sum of the two transitions for an interrogation time "t _int " in an interrogation step 220 as: | S ^A S ^B ) + e ^i(<M+<B), | D ^A D ^B . [0030] According to some embodiments, a detection step 230 may include the phase difference with respect to the local oscillator (such as the local oscillator 140 shown in Fig. 1) to be measured by a (global) π/2 carrier pulse 231 for A ⁺ ion 102, and a π/2 carrier pulse 232 for B ⁺ ion 103 for state detection (for each ion with its own laser, as shown in Fig. 1). In some embodiments, detection step 230 may be performed by a detector (such as detector 130 shown in Fig. 1). The detection step 230 may be followed by a parity analysis and/or computation step 240, in which:

[0031] According to some embodiments, the two-atom combination clock may behave like an atomic clock having a single atom with coo = (OA + ο¾ and with a measured error signal δο = 5A + δβ. In the case of two uncorrelated lasers it is sufficient to feed back on only one of them, assuming that the free-running laser has drifts which are much smaller than 1/x _p , where τ _ρ is the pulse duration in the operational sequence. In various embodiments, the issue of frequency stability may be manifested only in the sum of the two laser frequencies and not for each one separately, which in use can be obtained by sum-frequency generation with a nonlinear crystal.

[0032] In some embodiments, correlated lasers may be tuned via a frequency comb (e.g., such as frequency comb 108 shown in Fig. 1). The two laser frequencies may be (OA = n · COR and ο¾ = m · COR, where COR is the comb repetition, 'n' and 'm' are positive integers, and the offset frequency is zero. The error signal from interrogation step 220 may then be of the form δο = 5 _R (n +m), which is fed back to stabilize Q _R .

[0033] According to some embodiments, a quantum superposition of two different species, ⁴⁰ Ca ⁺ and ¹⁷⁴ Yb ⁺ may contribute to enhanced performance for the abovementioned structure. In some embodiments, a quantum superposition of one

88 Sr + ion and multiple (e.g., three) 202 Hg + ions may also contribute to enhanced performance for the abovementioned structure. These quantum superpositions may feature a reduction in the susceptibility of the reference frequency to changes in the environmental magnetic field and a reduction in the frequency shift caused by black body radiation.

40,

'Ca ⁺ - ¹⁷⁴ Yb ⁺ [0034] According to some embodiments, the atomic combination clock may utilize a combination of the electric quadrupole transition ⁴ Si _/2 ^→3 D _3/2 in ⁴⁰ Ca ⁺ and a similar electric quadrupole transition ⁶ Si _/2 → ⁵ D _3/2 in ¹⁷⁴ Yb ⁺ . This may be a particularly suitable combination since the two transitions are driven using easily-accessible wavelengths of 732 nanometers and 436 nanometers (nm) respectively, while the effective characteristic frequency of the superposition corresponds to a wavelength of 273 nm (or 1098 terahertz frequency). This effective wavelength is sufficiently close to that of the 27 Al + optical clock (267 nm) with the advantage that ultraviolet light is not needed to drive this transition. It should be noted that although the entangled superposition is characterized by ultraviolet wavelength at 273 nm, the combination clock (such as atomic combination clock 100 shown in Fig. 1) may be driven by two lasers at 732 nm and 436 nm, respectively. Furthermore, the magnetic moments of these two transitions are the same to within 10 ^" , so equal superpositions with opposite 'm' states can have almost zero magnetic susceptibility. Additionally, the differential static polarizabilities of these two transitions are very close in magnitude but may have opposite signs and therefore a superposition of the two also has a significantly smaller susceptibility to blackbody radiation, when adding the frequencies, as in the 8 °8°Sr + ^T - 3 case discussed further below. The specific supposition considered here is:

—j^ (| Ca ⁺ ; S _{1/2 1/2} ^| Yb ⁺ ; S _1/2 _ _1/2 ^ + | Ca ⁺ ; ϋ _{3/2 1/2} ^| Yb ⁺ ; D _3/2 _ _1/2 ^) (3)

[0035] It should be noted that these embodiments with specific quantum superpositions may illustrate a reference frequency that is characteristic of the quantum superposition of the atomic species, rather than the individual frequencies of the different species. The quantum superposition of the two species inherently has a characteristic frequency which is the sum of the individual characteristic frequencies.

88 _Sr+ _ 3 202 _Hg+

[0036] Reducing the frequency shift caused by black body radiation has been particularly difficult because once the polarizability is known it has typically required evaluation of the black body radiation fields with high accuracy. In some embodiments, a significant reduction may be achieved by minimizing the atomic species combination's differential scalar polarizability, when adding the frequencies, as in the ⁴⁰ Ca ⁺ - ¹⁷⁴ Yb ⁺ case discussed above. [0037] The differential polarizability of the S 1/2→ D5/2 electric quadrupole transition at 674 nm in ⁸⁸ Sr ⁺ is Δ¾ = -47.938 x 10 ^"41 Jm ² /V ² . The differential polarizability of the same transition in Hg at 282 nm is Δ¾ = +15 x 10 Jm /V . Thus, a superposition of a single 8 °8°Sr + ^T and three 2 "0 ^u 2¾g + ^T ions would significantly reduce Δ¾ .

[0038] It should be appreciated that while specific isotopes (e.g., ⁴⁰ Ca ⁺ , ¹⁷⁴ Yb ⁺ , ⁸⁸ Sr ⁺ and ²⁰² Hg ⁺ ) are described above, different combinations of atomic species and/or isotopes may also apply to create an efficient quantum superposition for the atomic combination clock.

[0039] It should be noted that in contrast to dual atomic clock systems using two atomic clocks in parallel (each atomic clock for a different atomic species, with a different frequency) in order to have a specific atomic reference, the atomic combination clock of the present invention (e.g., as shown in Fig. 1) provides an apparatus with a single atomic clock where the quantum superposition of a plurality of atomic species and/or isotopes allows accurate and stable clock readings.

[0040] Reference is now made to Fig. 3, which shows a flowchart for a method of operating an atomic combination clock, according to some embodiments. Each of the atomic species in the plurality of different atomic species may be initialized 301 and combined 302 in a quantum superposition. The combined atomic species may be interrogated 303 at a reference frequency that is characteristic of the quantum superposition. In some embodiments, the local oscillator (such as local oscillator 140 shown in Fig. 1) may be locked 304 to the reference frequency to output a corresponding clock time by translating counts of oscillator periods to time units.

[0041] Unless explicitly stated, the method embodiments described herein are not constrained to a particular order in time or chronological sequence. Additionally, some of the described method elements can be skipped, or they can be repeated, during a sequence of operations of a method.

[0042] Various embodiments have been presented. Each of these embodiments may of course include features from other embodiments presented, and embodiments not specifically described may include various features described herein.