Fast nuclear-spin gates and electrons−nuclei entanglement of neutral atoms in weak magnetic fields

doi:10.1007/s11467-023-1332-0

Front. Phys.

2024, Vol. 19

Issue (2) : 22203 https://doi.org/10.1007/s11467-023-1332-0

RESEARCH ARTICLE

Fast nuclear-spin gates and electrons−nuclei entanglement of neutral atoms in weak magnetic fields

Xiao-Feng Shi(

)

School of Physics, Xidian University, Xi’an 710071, China

Download: PDF(6849 KB) HTML
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

Abstract

We present a novel class of Rydberg-mediated nuclear-spin entanglement in divalent atoms with global laser pulses. First, we show a fast nuclear-spin controlled phase gate of an arbitrary phase realizable either with two laser pulses when assisted by Stark shifts, or with three pulses. Second, we propose to create an electrons−nuclei-entangled state, which is named a super bell state (SBS) for it mimics a large Bell state incorporating three small Bell states. Third, we show a protocol to create a three-atom electrons-nuclei entangled state which contains the three-body W and Greenberger−Horne−Zeilinger (GHZ) states simultaneously. These protocols possess high intrinsic fidelities, do not require single-site Rydberg addressing, and can be executed with large Rydberg Rabi frequencies in a weak, Gauss-scale magnetic field. The latter two protocols can enable measurement-based preparation of Bell, hyperentangled, and GHZ states, and, specifically, SBS can enable quantum dense coding where one can share three classical bits of information by sending one particle.

Keywords nuclear-spin qubit electrons−nuclei entanglement super Bell state Greenberger−Horne−Zeilinger state Rydberg-mediated entanglement quantum dense coding

Corresponding Author(s): Xiao-Feng Shi

Issue Date: 27 September 2023

Cite this article:

Xiao-Feng Shi. Fast nuclear-spin gates and electrons−nuclei entanglement of neutral atoms in weak magnetic fields[J]. Front. Phys. , 2024, 19(2): 22203.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-023-1332-0
https://academic.hep.com.cn/fop/EN/Y2024/V19/I2/22203

Fig.1 Rydberg excitation of two nuclear-spin qubit states

| ↑ ?

and

| ↓ ?

| c ↑ ? ≡ | (6 s 2) 3 P 0 | I = 1 / 2, m I = 1 / 2 ?

and

| c ↓ ? ≡ | (6 s 2) 3 P 0 | I = 1 / 2, m I = − 1 / 2 ?

to two respective Rydberg states

| r − ?

and

| r + ?

, where c denotes the clock state with ¹⁷¹Yb as an example. In a B-field of several Gauss (1 G=

10 − 4

T), the two nuclear spin states in the clock state are nearly degenerate compared to the MHz-scale Rabi frequencies considered in this paper. The laser fields are

π

polarized and tuned to the middle of the gap between

| r + ?

and

| r − ?

Fig.2 State dynamics for different input states when ignoring Rydberg-state decay in the controlled-phase gate (with

β = − π

as an example here). (a)

| Ω x | / Δ

as a function of time during the three pulses of the nuclear-spin gate. Here, the largest Rabi frequency is

| Ω 1 | = | Ω 3 | = 2 π × 3.25

MHz, and the relative phases of the three Rabi frequencies are

0, 3 π / 4, − π / 2

. The Rydberg interaction is

V 0 / (2 π) = 260

MHz (its fluctuation is studied in Section 2.4). (b−d) show the population and phase of the ground-state component in the wavefunction when the input states for the gate protocol are

| c ↑ c ↑ ?

| c ↑ c ↓ ?

, and

| c ↓ c ↓ ?

, respectively. The final population errors in the target ground states are

2.6 × 10 − 5

2.1 × 10 − 5

, and

2.4 × 10 − 5

in (b), (c), and (d), respectively, and their final phases are

− 1.771

1.587

, and

1.816

rad, respectively. The state dynamics for the input state

| c ↓ c ↑ ?

is similar to that of

| c ↑ c ↓ ?

Fig.3 Rotation error of the nuclear-spin gate (scaled by

105

) of Eq. (10) averaged by uniformly varying the Rydberg interaction

V

[(1 − ?) V 0, (1 + ?) V 0]

, where

V 0 / (2 π) = 260

MHz. The fluctuation of

V

leads to phases different from the desired phases in Eq. (9). The largest Rabi frequency in the simulation is

| Ω 1 | / (2 π) = 3.25

MHz shown in Fig.2(a). The gate fidelity

1 − E ¯ r o − E d e c a y

is over

0.995

for the

?

shown here, where the gate error is dominated by

E d e c a y = 4.15 × 10 − 3

due to the short Rydberg state lifetime

τ = 100

μs.

		First pulse	Second pulse	Third pulse	Total duration

Three-pulse gate	Rabi frequency	$1.6088 Δ$	$0.5932 e i 3 π / 4 Δ$	$1.6088 e i β / 2 Δ$	$3.14 π / Δ$
Three-pulse gate	pulse duration	$0.805 π / Δ$	$1.532 π / Δ$	$0.805 π / Δ$	or $5.05 π / Ω m$
Two-pulse gate	Rabi frequency	$1.6088 Δ$	$− 1.6088 e i (β / 2 + κ) Δ$	(not applicable)	$1.61 π / Δ$
Two-pulse gate	pulse duration	$0.805 π / Δ$	$0.805 π / Δ$	(not applicable)	or $2.59 π / Ω m$

Tab.1 Parameters for creating nuclear-spin controlled-phase gate of phase

β

. In the ideal blockade condition the gate map is diag

{e − i α, e − i β / 2, e − i β / 2, e i α}

, where

α

is about 1.79 rad in the three-pulse gate, and is zero in the two-pulse gate. A CZ gate is realized via single-qubit rotations when choosing

β = π

for both cases here.

κ

is a phase to compensate an overall phase factor in the frame transform as discussed around Eq. (12).

Fig.4 State dynamics of the two-pulse nuclear-spin gate with

β = π

and

| Ω 2 | = Ω 1 ≈ 2 π × 3.25

MHz as an example. (a) The two laser pulses have the same strength and duration. The relative phase of the two Rabi frequencies are

0

and

π / 2 + κ

, where

κ

is given above Eq. (12). A Stark shift

4 Δ ≈ 8.08

MHz was assumed in

| r − ?

during the second pulse, and the frequency of the laser during the second pulse increases by

2 Δ

compared to the first pulse. The Rydberg interaction is

V 0 / (2 π) = 260

MHz. (b−d) show the population and phase of the ground-state component in the wavefunction when the input states for the gate protocol are

| c ↑ c ↑ ?

| c ↑ c ↓ ?

, and

| c ↓ c ↓ ?

, respectively. The final population errors in the target ground states are

4.4 × 10 − 5

1.24 × 10 − 4

, and

4.4 × 10 − 5

in (a), (b), and (c), respectively, and their final phases are

0.0213

− 1.5583

, and

0.0213

rad, respectively.

Fig.5 Rotation error of the nuclear-spin gate (scaled by

104

) averaged by uniformly varying the Rydberg interaction

V

[(1 − ?) V 0, (1 + ?) V 0]

, where

V 0 / (2 π) = 260

MHz. Other parameters are the same as in Fig.4. The gate fidelity

1 − E ¯ r o − E d e c a y

is over

0.997

for the

?

shown here, where the gate error is dominated by

E d e c a y = 2.26 × 10 − 3

Fig.6 State dynamics of the SBS protocol for different input states with

V 0 / (2 π) = 260

MHz and maximal Rabi frequency

Ω (S) / (2 π) ≈ 2.28

MHz when ignoring Rydberg-state decay. (a) Magnitudes of Rabi frequencies in units of

Δ

. Here, the third pulse is with two-photon laser excitation, where one laser is resonant for the transition

| g ↑ ? → | r + ?

and the other laser resonant for

| g ↓ ? → | r − ?

, each with a Rabi frequency

Ω e f f = 2 π × 1

MHz. These two lasers can be from one laser source via pulse pickers for shifting the frequency of one sub-beam by

2 Δ

. (b−d) show the population of the ground-state component in the wavefunction when the input states for the SBS protocol are

| c ↑ c ↑ ?

| c ↑ c ↓ ?

, and

| c ↓ c ↓ ?

, respectively. The thin (thick) curves in (b) and (d) denote population in the product (Bell) states. For the target ground states

| Φ ? e ⊗ | ↑↑ ? n

in (b),

| c ↑ c ↓ ?

in (c), and

| Φ ? e ⊗ | ↓↓ ? n

in (d), the final populations are

1 − 1.4 × 10 − 4

1 − 3.1 × 10 − 5

, and

1 − 5.5 ×

10 − 5

respectively, and the final phases are

Δ [T p 1 ({S}) + T p 2 ({S})] −

2.406

rad,

0.009

rad, and

− Δ [T p 1 ({S}) + T p 2 ({S})] − 0.697

rad, respectively. These are different from those described in Sections 4.1.2 and 4.1.3 for the Rydberg interaction here is finite (its fluctuation is studied in Section 4.2).

Fig.7 Rotation error (scaled by

104

) of Eq. (26) averaged by uniformly varying the Rydberg interaction

V

[(1 − ?) V 0, (1 + ?) V 0]

for creating SBS. Here,

V 0 / (2 π) = 260

MHz,

Ω e f f / (2 π) = 1

MHz, and

Ω (S)

and

Δ

are given by Eqs. (18) and (19). The fidelity of SBS generation,

1 − E ¯ r o − E d e c a y

, is about

0.992

dominated by the Rydberg-state decay

E d e c a y = 7.51 ×

10 − 3

due to the short Rydberg state lifetime

τ = 100 μ

	Initial state	Final state	First pulse (clock-Rydberg)	Second pulse (clock-Rydberg)	Third pulse (ground-Rydberg)	Total duration

$\| S B ?$	$∏ \| c ↑ ? + \| c ↓ ? 2$	$12 (\| c c ? e ⊗ \| Φ ? n$ $+ \| Φ ? e ⊗ \| Ψ ? n)$	Rabi: $Ω (S) = 1.608 Δ$ $T p 1 : 2.12 π / Ω (S)$	Rabi: $− 0.4606 Ω (S)$ $T p 2 : 2.85 π / Ω (S)$	Rabi: $0.4393 Ω (S)$ $T p 3 : 2.71 π / Ω (S)$	$7.69 π / Ω (S)$
$\| ? ?$	$∏ \| c ↑ ? + \| c ↓ ? 2$	$12 [(3 \| c c c ? e ⊗ \| ? ? n$ $+ \| W ? e ⊗ \| G H Z ? n)]$	Rabi: $Ω (?) = 1.976 Δ$ $T p 1 (?)$ : $5.93 π / Ω (?)$	Rabi: $− 0.3735 Ω (?)$ $T p 2 (?) : 1.9 π / Ω (?)$	Rabi: $0.3073 Ω (?)$ $T p 3 (?)$ : $3.54 π / Ω (?)$	$11.4 π / Ω (?)$

Tab.2 Parameters for creating the two-atom super Bell state of Eq. (1) and the three-atom entangled state of Eq. (3).

Fig.8 State dynamics of the

| ? ?

protocol for different input states with

V 0 / (2 π) = 260

MHz and maximal Rabi frequency

Ω (?) / (2 π) ≈ 3.25

MHz when ignoring Rydberg-state decay. (a) Magnitudes of Rabi frequencies in units of

Δ

. (b−e) show the population of the ground-state component in the wavefunction when the input states for the gate protocol are

| c ↑ c ↑ c ↑ ?

| c ↑ c ↑ c ↓ ?, | c ↓ c ↓ c ↑ ?

, and

| c ↓ c ↓ c ↓ ?

, respectively. The thin and thick curves in (b) and (e) denote population in the product and W states, respectively. For the target ground states

| W ? e ⊗ | ↑↑↑ ? n

in (b),

| c ↑ c ↑ c ↓ ?

in (c),

| c ↓ c ↓ c ↑ ?

in (d), and

| W ? e ⊗ | ↓↓↓ ? n

in (e), the final populations are

0.9986

0.9968

0.9988

, and

0.9982

respectively, and the final phases are

ϑ 1 = Δ [T p 1 (?) + T p 2 (?)] − 2.532

rad,

ϑ 2 = − 0.7648

rad,

ϑ 3 = 0.9795

rad, and

ϑ 4 = − Δ [T p 1 (?) + T p 2 (?)] − 0.385

rad, respectively.

Fig.9 Rotation error (scaled by

103

) averaged by uniformly varying the Rydberg interaction

V

[(1 − ?) V 0, (1 + ?) V 0]

for creating

| ? ?

. Here,

V 0 / (2 π) = 260

MHz,

Ω e f f (?) / (2 π) = 1

MHz, and

Ω (?)

and

Δ

are given by Eqs. (31) and (32). The fidelity to generate

| ? ?

in the form of Eq. (33),

1 − E ¯ r o − E d e c a y

, is about

0.988

for

? = 0.8

Fig.10 Scheme for mapping atomic states to photons. (a) An atom is placed inside a Fabry−Perot resonator. The quantization axis is along

z

specified by an external magnetic field

B z

. Laser fields sent along

x

y

directions can couple the ground or clock states of the atoms to

6 s 5 d 3 D 1, F = 3 / 2

. (b) The two ground Zeeman substates

| g ↑ ?

and

| g ↓ ?

are coupled to the

m F = 3 / 2

and

m F = − 3 / 2

states of

6 s 5 d 3 D 1, F = 3 / 2

via the intermediate state

6 s 6 p 3 P 1

. The detuning at

6 s 6 p 3 P 1

is large compared to the Zeeman splitting which is not shown in the figure. The lower transition is with a

z

-polarized field, and the upper field is

x

-polarized. The dashed arrows show transitions largely detuned so that no transition occurs there. (c) The two nuclear-spin substates

| c ↑ ?

and

| c ↓ ?

are coupled to the

m F = 3 / 2

and

m F = − 3 / 2

states of

6 s 5 d 3 D 1, F = 3 / 2

. Dashed arrows indicate detuned transitions where no population transfer occurs. (d) The cavity mode is nearly resonant with the transition

6 s 5 d 3 D 1, F = 3 / 2 ↔ 6 s 6 p 3 P 1, F = 1 / 2

, in which the g factor of the lower state is nearly six times that of the upper state, and the Zeeman splitting between the two transitions indicated by the two arrows is about

μ B B

, which is supposed to be small compared to the cavity linewidth. We assume that the cavity photon is coupled almost perfectly to an optical fibre which is not shown here. Mapping of the the SBS state of atoms to that of photons proceeds as follows. (i) Move the two atoms to two cavities; (ii) The processes in (b) and (d) map the nuclear-spin states in the ground-state atoms to polarization qubits of photons; (iii) Use (c) and (d) to map the nuclear-spin states in the clock-state atoms to polarization qubits of photons. Because of the time gap between the steps (ii) and (iii), the “g” and “c” degree of freedom of atoms is mapped to the time-bin degree of freedom of photons.

Fig. E1State dynamics of the

| ? ?

protocol with a faster speed with

V 0 / (2 π) = 260

MHz and maximal Rabi frequency

Ω (?) / (2 π) ≈ 3.25

MHz when ignoring Rydberg-state decay. The meaning of the contents are the same as those in Fig.8. In (b) and (e), there is some population not transferred to the Rydberg state at the end of the second pulse, which results in a larger error of the entanglement generation compared to the case described around Fig.8.

Fig. E2 Rotation error (scaled by

100

) averaged by uniformly varying the Rydberg interaction

V

[(1 − ?) V 0, (1 + ?) V 0]

for creating

| ? ?

with the parameters of Fig. E1 and Appendix E. The fidelity to generate

| ? ?

in the form similar to that in Eq. (33),

1 − E ¯ r o − E d e c a y

, is about

0.972

for

? = 0.8

1	Jaksch D., I. Cirac J., Zoller P., L. Rolston S., Cote R., D. Lukin M.. Fast quantum gates for neutral atoms. Phys. Rev. Lett., 2000, 85(10): 2208 https://doi.org/10.1103/PhysRevLett.85.2208
2	D. Lukin M., Fleischhauer M., Cote R., M. Duan L., Jaksch D., I. Cirac J., Zoller P.. Dipole blockade and quantum information processing in mesoscopic atomic ensembles. Phys. Rev. Lett., 2001, 87(3): 037901 https://doi.org/10.1103/PhysRevLett.87.037901
3	Wilk T., Gaetan A., Evellin C., Wolters J., Miroshnychenko Y., Grangier P., Browaeys A.. Entanglement of two individual neutral atoms using Rydberg blockade. Phys. Rev. Lett., 2010, 104(1): 010502 https://doi.org/10.1103/PhysRevLett.104.010502
4	Isenhower L., Urban E., L. Zhang X., T. Gill A., Henage T., A. Johnson T., G. Walker T., Saffman M.. Demonstration of a neutral atom controlled-NOT quantum gate. Phys. Rev. Lett., 2010, 104(1): 010503 https://doi.org/10.1103/PhysRevLett.104.010503
5	L. Zhang X., Isenhower L., T. Gill A., G. Walker T., Saffman M.. Deterministic entanglement of two neutral atoms via Rydberg blockade. Phys. Rev. A, 2010, 82: 030306(R) https://doi.org/10.1103/PhysRevA.82.030306
6	M. Maller K., T. Lichtman M., Xia T., Sun Y., J. Piotrowicz M., W. Carr A., Isenhower L., Saffman M.. Rydberg-blockade controlled-not gate and entanglement in a two-dimensional array of neutral-atom qubits. Phys. Rev. A, 2015, 92(2): 022336 https://doi.org/10.1103/PhysRevA.92.022336
7	Y. Jau Y., M. Hankin A., Keating T., H. Deutsch I., W. Biedermann G.. Entangling atomic spins with a Rydberg-dressed spin-flip blockade. Nat. Phys., 2016, 12(1): 71 https://doi.org/10.1038/nphys3487
8	Zeng Y., Xu P., He X., Liu Y., Liu M., Wang J., J. Papoular D., V. Shlyapnikov G., Zhan M.. Entangling two individual atoms of different isotopes via Rydberg blockade. Phys. Rev. Lett., 2017, 119(16): 160502 https://doi.org/10.1103/PhysRevLett.119.160502
9	Levine H., Keesling A., Omran A., Bernien H., Schwartz S., S. Zibrov A., Endres M., Greiner M., Vuletíc V., D. Lukin M.. High-fidelity control and entanglement of Rydberg atom qubits. Phys. Rev. Lett., 2018, 121(12): 123603 https://doi.org/10.1103/PhysRevLett.121.123603
10	J. Picken C., Legaie R., McDonnell K., D. Pritchard J.. Entanglement of neutral-atom qubits with long ground-Rydberg coherence times. Quantum Sci. Technol., 2018, 4(1): 015011 https://doi.org/10.1088/2058-9565/aaf019
11	Levine H., Keesling A., Semeghini G., Omran A., T. Wang T., Ebadi S., Bernien H., Greiner M., Vuletíc V., Pichler H., D. Lukin M.. Parallel implementation of high-fidelity multi-qubit gates with neutral atoms. Phys. Rev. Lett., 2019, 123(17): 170503 https://doi.org/10.1103/PhysRevLett.123.170503
12	M. Graham T., Kwon M., Grinkemeyer B., Marra Z., Jiang X., T. Lichtman M., Sun Y., Ebert M., Saffman M.. Rydberg mediated entanglement in a two-dimensional neutral atom qubit array. Phys. Rev. Lett., 2019, 123(23): 230501 https://doi.org/10.1103/PhysRevLett.123.230501
13	Jo H., Song Y., Kim M., Ahn J.. Rydberg atom entanglements in the weak coupling regime. Phys. Rev. Lett., 2020, 124(3): 033603 https://doi.org/10.1103/PhysRevLett.124.033603
14	Fu Z., Xu P., Sun Y., Y. Liu Y., D. He X., Li X., Liu M., B. Li R., Wang J., Liu L., S. Zhan M.. High-fidelity entanglement of neutral atoms via a Rydberg-mediated single-modulated-pulse controlled-PHASE gate. Phys. Rev. A, 2022, 105(4): 042430 https://doi.org/10.1103/PhysRevA.105.042430
15	McDonnell K., F. Keary L., D. Pritchard J.. Demonstration of a quantum gate using electromagnetically induced transparency. Phys. Rev. Lett., 2022, 129(20): 200501 https://doi.org/10.1103/PhysRevLett.129.200501
16	Bluvstein D., Levine H., Semeghini G., T. Wang T., Ebadi S., Kalinowski M., Keesling A., Maskara N., Pichler H., Greiner M., Vuleti’c V., D. Lukin M.. A quantum processor based on coherent transport of entangled atom arrays. Nature, 2022, 604(7906): 451 https://doi.org/10.1038/s41586-022-04592-6
17	M. Graham T., Song Y., Scott J., Poole C., Phuttitarn L., Jooya K., Eichler P., Jiang X., Marra A., Grinkemeyer B., Kwon M., Ebert M., Cherek J., T. Lichtman M., Gillette M., Gilbert J., Bowman D., Ballance T., Campbell C., D. Dahl E., Crawford O., S. Blunt N., Rogers B., Noel T., Saffman M.. Multi-qubit entanglement and algorithms on a neutral-atom quantum computer. Nature, 2022, 604(7906): 457 https://doi.org/10.1038/s41586-022-04603-6
18	J. Evered S.Bluvstein D.Kalinowski M.Ebadi S.Manovitz T. Zhou H.H. Li S.A. Geim A.T. Wang T.Maskara N. Levine H.Semeghini G.Greiner M.Vuletic V.D. Lukin M., High-fidelity parallel entangling gates on a neutral atom quantum computer, arXiv: 2304.05420v1 (2023)
19	S. Madjarov I., P. Covey J., L. Shaw A., Choi J., Kale A., Cooper A., Pichler H., Schkolnik V., R. Williams J., Endres M.. High-fidelity entanglement and detection of alkaline-earth Rydberg atoms. Nat. Phys., 2020, 16(8): 857 https://doi.org/10.1038/s41567-020-0903-z
20	Ma S., P. Burgers A., Liu G., Wilson J., Zhang B., D. Thompson J.. Universal gate operations on nuclear spin qubits in an optical tweezer array of 171Yb atoms. Phys. Rev. X, 2022, 12(2): 021028 https://doi.org/10.1103/PhysRevX.12.021028
21	Schine N., W. Young A., J. Eckner W., J. Martin M., M. Kaufman A.. Long-lived Bell states in an array of optical clock qubits. Nat. Phys., 2022, 18(9): 1067 https://doi.org/10.1038/s41567-022-01678-w
22	Scholl P.L. Shaw A.B. S. Tsai R.Finkelstein R.Choi J. Endres M., Erasure conversion in a high-fidelity Rydberg quantum simulator, arXiv: 2305.03406v1 (2023)
23	Ma S.Liu G. Peng P.Zhang B.Jandura S.P. Burgers A.Pupillo G. Puri S.D. Thompson J., High-fidelity gates with mid-circuit erasure conversion in a metastable neutral atom qubit, arXiv: 2305.05493v1 (2023)
24	Yamamoto R., Kobayashi J., Kuno T., Kato K., Takahashi Y.. An ytterbium quantum gas microscope with narrow-line laser cooling. New J. Phys., 2016, 18(2): 023016 https://doi.org/10.1088/1367-2630/18/2/023016
25	Saskin S., T. Wilson J., Grinkemeyer B., D. Thompson J.. Narrow-line cooling and imaging of ytterbium atoms in an optical tweezer array. Phys. Rev. Lett., 2019, 122(14): 143002 https://doi.org/10.1103/PhysRevLett.122.143002
26	Cooper A., P. Covey J., S. Madjarov I., G. Porsev S., S. Safronova M., Endres M.. Alkaline-earth atoms in optical tweezers. Phys. Rev. X, 2018, 8(4): 041055 https://doi.org/10.1103/PhysRevX.8.041055
27	A. Norcia M., W. Young A., M. Kaufman A.. Microscopic control and detection of ultracold strontium in optical-tweezer arrays. Phys. Rev. X, 2018, 8(4): 041054 https://doi.org/10.1103/PhysRevX.8.041054
28	P. Covey J., S. Madjarov I., Cooper A., Endres M.. 2000-times repeated imaging of strontium atoms in clock-magic tweezer arrays. Phys. Rev. Lett., 2019, 122(17): 173201 https://doi.org/10.1103/PhysRevLett.122.173201
29	T. Wilson J., Saskin S., Meng Y., Ma S., Dilip R., P. Burgers A., D. Thompson J.. Trapping alkaline earth Rydberg atoms optical tweezer arrays. Phys. Rev. Lett., 2022, 128(3): 033201 https://doi.org/10.1103/PhysRevLett.128.033201
30	J. Daley A., M. Boyd M., Ye J., Zoller P.. Quantum computing with alkaline-earth-metal atoms. Phys. Rev. Lett., 2008, 101(17): 170504 https://doi.org/10.1103/PhysRevLett.101.170504
31	V. Gorshkov A., M. Rey A., J. Daley A., M. Boyd M., Ye J., Zoller P., D. Lukin M.. Alkaline-earth-metal atoms as few-qubit quantum registers. Phys. Rev. Lett., 2009, 102(11): 110503 https://doi.org/10.1103/PhysRevLett.102.110503
32	Reichenbach I., H. Deutsch I.. Sideband cooling while preserving coherences in the nuclear spin state in group-II-like atoms. Phys. Rev. Lett., 2007, 99(12): 123001 https://doi.org/10.1103/PhysRevLett.99.123001
33	F. Shi X.. Coherence-preserving cooling of nuclear-spin qubits in a weak magnetic field. Phys. Rev. A, 2023, 107(2): 023102 https://doi.org/10.1103/PhysRevA.107.023102
34	Omanakuttan S., Mitra A., J. Martin M., H. Deutsch I.. Quantum optimal control of ten-level nuclear spin qudits in 87Sr. Phys. Rev. A, 2021, 104(6): L060401 https://doi.org/10.1103/PhysRevA.104.L060401
35	Chen N., Li L., Huie W., Zhao M., Vetter I., H. Greene C., P. Covey J.. Analyzing the Rydberg-based optical-metastable-ground architecture for 171Yb nuclear spins. Phys. Rev. A, 2022, 105(5): 052438 https://doi.org/10.1103/PhysRevA.105.052438
36	M. Boyd M., Zelevinsky T., D. Ludlow A., Blatt S., Zanon-Willette T., M. Foreman S., Ye J.. Nuclear spin effects in optical lattice clocks. Phys. Rev. A, 2007, 76(2): 022510 https://doi.org/10.1103/PhysRevA.76.022510
37	F. Shi X.. Rydberg quantum computation with nuclear spins in two-electron neutral atoms. Front. Phys., 2021, 16(5): 52501 https://doi.org/10.1007/s11467-021-1069-6
38	F. Shi X.. Fast, accurate, and realizable two-qubit entangling gates by quantum interference in detuned Rabi cycles of Rydberg atoms. Phys. Rev. Appl., 2019, 11(4): 044035 https://doi.org/10.1103/PhysRevApplied.11.044035
39	Barnes K., Battaglino P., J. Bloom B., Cassella K., Coxe N., Crisosto N., P. King J., S. Kondov S., Kotru K., C. Larsen S., Lauigan J., J. Lester B., McDonald M., Megidish E., Narayanaswami S., Nishiguchi C., Notermans R., S. Peng L., Ryou A., Y. Wu T., Yarwood M.. Assembly and coherent control of a register of nuclear spin qubits. Nat. Commun., 2022, 13(1): 2779 https://doi.org/10.1038/s41467-022-29977-z
40	Jenkins A., W. Lis J., Senoo A., F. McGrew W., M. Kaufman A.. Ytterbium nuclear-spin qubits in an optical tweezer array. Phys. Rev. X, 2022, 12(2): 021027 https://doi.org/10.1103/PhysRevX.12.021027
41	H. Bennett C., J. Wiesner S.. Communication via one- and two-particle operators on Einstein−Podolsky−Rosen states. Phys. Rev. Lett., 1992, 69(20): 2881 https://doi.org/10.1103/PhysRevLett.69.2881
42	Dür W., Vidal G., I. Cirac J.. Three qubits can be entangled in two inequivalent ways. Phys. Rev. A, 2000, 62(6): 062314 https://doi.org/10.1103/PhysRevA.62.062314
43	Fang B., Menotti M., Liscidini M., E. Sipe J., O. Lorenz V.. Three-photon discrete-energy-entangled W state in an optical fiber. Phys. Rev. Lett., 2019, 123(7): 070508 https://doi.org/10.1103/PhysRevLett.123.070508
44	M. Greenberger D.Horne M.Zeilinger A., Bell’s Theorem, Quantum Theory, and Conceptions of the Universe, edited by M. Kafatos, Kluwer, Dordrecht, 1989
45	F. Shi X.. Hyperentanglement of divalent neutral atoms by Rydberg blockade. Phys. Rev. A, 2021, 104(4): 042422 https://doi.org/10.1103/PhysRevA.104.042422
46	Saffman M., G. Walker T., Mølmer K.. Quantum information with Rydberg atoms. Rev. Mod. Phys., 2010, 82(3): 2313 https://doi.org/10.1103/RevModPhys.82.2313
47	F. Shi X.. Quantum logic and entanglement by neutral Rydberg atoms: Methods and fidelity. Quantum Sci. Technol., 2022, 7(2): 023002 https://doi.org/10.1088/2058-9565/ac18b8
48	P. Burgers A., Ma S., Saskin S., Wilson J., A. Alarcón M., H. Greene C., D. Thompson J.. Controlling Rydberg excitations using ion core transitions in alkaline earth atom tweezer arrays. PRX Quantum, 2022, 3(2): 020326 https://doi.org/10.1103/PRXQuantum.3.020326
49	Ding R., D. Whalen J., K. Kanungo S., C. Killian T., B. Dunning F., Yoshida S., Burgdörfer J.. Spectroscopy of 87Sr triplet Rydberg states. Phys. Rev. A, 2018, 98(4): 042505 https://doi.org/10.1103/PhysRevA.98.042505
50	Lurio A., Mandel M., Novick R.. Second-order hyperfine and Zeeman corrections for an (sl) configuration. Phys. Rev., 1962, 126(5): 1758 https://doi.org/10.1103/PhysRev.126.1758
51	F. Shi X.. Rydberg quantum gates free from blockade error. Phys. Rev. Appl., 2017, 7(6): 064017 https://doi.org/10.1103/PhysRevApplied.7.064017
52	F. Shi X.. Accurate quantum logic gates by spin echo in Rydberg atoms. Phys. Rev. Appl., 2018, 10(3): 034006 https://doi.org/10.1103/PhysRevApplied.10.034006
53	P. Williams C., Explorations in Quantum Computing, 2nd Ed., edited by D. Gries and F. B. Schneider, Texts in Computer Science, Springer-Verlag, London, 2011
54	Saffman M., G. Walker T.. Analysis of a quantum logic device based on dipole−dipole interactions of optically trapped Rydberg atoms. Phys. Rev. A, 2005, 72(2): 022347 https://doi.org/10.1103/PhysRevA.72.022347
55	H. Pedersen L., M. Møller N., Mølmer K.. Fidelity of quantum operations. Phys. Lett. A, 2007, 367(1−2): 47 https://doi.org/10.1016/j.physleta.2007.02.069
56	F. Shi X.. Deutsch, Toffoli, and CNOT gates via rydberg blockade of neutral atoms. Phys. Rev. Appl., 2018, 9: 051001(R) https://doi.org/10.1103/PhysRevApplied.9.051001
57	F. Shi X.. Transition slow-down by Rydberg interaction of neutral atoms and a fast controlled-NOT quantum gate. Phys. Rev. Appl., 2020, 14(5): 054058 https://doi.org/10.1103/PhysRevApplied.14.054058
58	L. Wu J., Wang Y., X. Han J., L. Su S., Xia Y., Jiang Y., Song J.. Unselective ground-state blockade of Rydberg atoms for implementing quantum gates. Front. Phys., 2022, 17(2): 22501 https://doi.org/10.1007/s11467-021-1104-7
59	Liu S., H. Shen J., H. Zheng R., H. Kang Y., C. Shi Z., Song J., Xia Y.. Optimized nonadiabatic holonomic quantum computation based on Förster resonance in Rydberg atoms. Front. Phys., 2022, 17(2): 21502 https://doi.org/10.1007/s11467-021-1108-3
60	M. Stojanović V., K. Nauth J.. Interconversion of W and Greenberger−Horne−Zeilinger states for Ising-coupled qubits with transverse global control. Phys. Rev. A, 2022, 106(5): 052613 https://doi.org/10.1103/PhysRevA.106.052613
61	Wu X., Liang X., Tian Y., Yang F., Chen C., C. Liu Y., K. Tey M., You L.. A concise review of Rydberg atom based quantum computation and quantum simulation. Chin. Phys. B, 2021, 30(2): 020305 https://doi.org/10.1088/1674-1056/abd76f
62	R. Chong D., Kim M., Ahn J., Jeong H.. Machine learning identification of symmetrized base states of Rydberg atoms. Front. Phys., 2022, 17(1): 12504 https://doi.org/10.1007/s11467-021-1099-0
63	Zhang H., Wu J., Artoni M., C. La Rocca G.. Single-photon-level light storage with distributed Rydberg excitations in cold atoms. Front. Phys., 2022, 17(2): 22502 https://doi.org/10.1007/s11467-021-1105-6
64	P. Covey J., Sipahigil A., Szoke S., Sinclair N., Endres M., Painter O.. Telecom-band quantum optics with ytterbium atoms and silicon nanophotonics. Phys. Rev. Appl., 2019, 11(3): 034044 https://doi.org/10.1103/PhysRevApplied.11.034044
65	D. Boozer A., Boca A., Miller R., E. Northup T., J. Kimble H.. Reversible state transfer between light and a single trapped atom. Phys. Rev. Lett., 2007, 98(19): 193601 https://doi.org/10.1103/PhysRevLett.98.193601
66	Wu Y., Kolkowitz S., Puri S., D. Thompson J.. Erasure conversion for fault-tolerant quantum computing in alkaline earth Rydberg atom arrays. Nat. Commun., 2022, 13(1): 4657 https://doi.org/10.1038/s41467-022-32094-6
67	Mitra A., J. Martin M., W. Biedermann G., M. Marino A., M. Poggi P., H. Deutsch I.. Robust Mølmer−Sørensen gate for neutral atoms using rapid adiabatic Rydberg dressing. Phys. Rev. A, 2020, 101: 030301(R) https://doi.org/10.1103/PhysRevA.101.030301
68	L. Pham K., F. Gallagher T., Pillet P., Lepoutre S., Cheinet P.. A coherent light shift on alkaline-earth Rydberg atoms from isolated core excitation without auto-ionization. PRX Quantum, 2022, 3(2): 020327 https://doi.org/10.1103/PRXQuantum.3.020327

[1]	Fan Li, Xiaoli Zhang, Jianbo Li, Jiawei Wang, Shaoping Shi, Long Tian, Yajun Wang, Lirong Chen, Yaohui Zheng. Demonstration of fully-connected quantum communication network exploiting entangled sideband modes[J]. Front. Phys. , 2023, 18(4): 42303-.
[2]	Jin-Xuan Han, Jin-Lei Wu, Zhong-Hui Yuan, Yan Xia, Yong-Yuan Jiang, Jie Song. Fast topological pumping for the generation of large-scale Greenberger−Horne−Zeilinger states in a superconducting circuit[J]. Front. Phys. , 2022, 17(6): 62504-.

Viewed

Full text

Abstract

Cited

Shared

Discussed