Quantum-enhanced sensing of displacements and electric fields with two-dimensional trapped-ion crystals
Quantum enhanced sensing
Harnessing quantum mechanical effects is expected to provide an advantage over classical sensing technology. By entangling the center-of-mass motional state of approximately 150 ions trapped in a two-dimensional Coulomb crystal with their collective spin state, Gilmore et al. demonstrate a quantum-enhanced measurement sensitivity of displacement and electric field. Such enhanced sensitivity could, for instance, find application in probing proposed weak interactions between dark matter and normal matter, as well as enhancing gravitational wave detection. —ISO
Abstract
Fully controllable ultracold atomic systems are creating opportunities for quantum sensing, yet demonstrating a quantum advantage in useful applications by harnessing entanglement remains a challenging task. Here, we realize a many-body quantum-enhanced sensor to detect displacements and electric fields using a crystal of ~150 trapped ions. The center-of-mass vibrational mode of the crystal serves as a high-Q mechanical oscillator, and the collective electronic spin serves as the measurement device. By entangling the oscillator and collective spin and controlling the coherent dynamics via a many-body echo, a displacement is mapped into a spin rotation while avoiding quantum back-action and thermal noise. We achieve a sensitivity to displacements of 8.8 ± 0.4 decibels below the standard quantum limit and a sensitivity for measuring electric fields of 240 ± 10 nanovolts per meter in 1 second. Feasible improvements should enable the use of trapped ions in searches for dark matter.
Get full access to this article
View all available purchase options and get full access to this article.
Already a Subscriber?Sign In
Supplementary Material
Supplementary Text
Figs. S1 to S11
References and Notes
1
J. P. Dowling, G. J. Milburn, Quantum technology: The second quantum revolution. Philos. Trans. R. Soc. A 361, 1655–1674 (2003).
2
C. L. Degen, F. Reinhard, P. Cappellaro, Quantum sensing. Rev. Mod. Phys. 89, 035002 (2017).
3
M. Tse, H. Yu, N. Kijbunchoo, A. Fernandez-Galiana, P. Dupej, L. Barsotti, C. D. Blair, D. D. Brown, S. E. Dwyer, A. Effler, M. Evans, P. Fritschel, V. V. Frolov, A. C. Green, G. L. Mansell, F. Matichard, N. Mavalvala, D. E. McClelland, L. McCuller, T. McRae, J. Miller, A. Mullavey, E. Oelker, I. Y. Phinney, D. Sigg, B. J. J. Slagmolen, T. Vo, R. L. Ward, C. Whittle, R. Abbott, C. Adams, R. X. Adhikari, A. Ananyeva, S. Appert, K. Arai, J. S. Areeda, Y. Asali, S. M. Aston, C. Austin, A. M. Baer, M. Ball, S. W. Ballmer, S. Banagiri, D. Barker, J. Bartlett, B. K. Berger, J. Betzwieser, D. Bhattacharjee, G. Billingsley, S. Biscans, R. M. Blair, N. Bode, P. Booker, R. Bork, A. Bramley, A. F. Brooks, A. Buikema, C. Cahillane, K. C. Cannon, X. Chen, A. A. Ciobanu, F. Clara, S. J. Cooper, K. R. Corley, S. T. Countryman, P. B. Covas, D. C. Coyne, L. E. H. Datrier, D. Davis, C. Di Fronzo, J. C. Driggers, T. Etzel, T. M. Evans, J. Feicht, P. Fulda, M. Fyffe, J. A. Giaime, K. D. Giardina, P. Godwin, E. Goetz, S. Gras, C. Gray, R. Gray, A. Gupta, E. K. Gustafson, R. Gustafson, J. Hanks, J. Hanson, T. Hardwick, R. K. Hasskew, M. C. Heintze, A. F. Helmling-Cornell, N. A. Holland, J. D. Jones, S. Kandhasamy, S. Karki, M. Kasprzack, K. Kawabe, P. J. King, J. S. Kissel, R. Kumar, M. Landry, B. B. Lane, B. Lantz, M. Laxen, Y. K. Lecoeuche, J. Leviton, J. Liu, M. Lormand, A. P. Lundgren, R. Macas, M. MacInnis, D. M. Macleod, S. Márka, Z. Márka, D. V. Martynov, K. Mason, T. J. Massinger, R. McCarthy, S. McCormick, J. McIver, G. Mendell, K. Merfeld, E. L. Merilh, F. Meylahn, T. Mistry, R. Mittleman, G. Moreno, C. M. Mow-Lowry, S. Mozzon, T. J. N. Nelson, P. Nguyen, L. K. Nuttall, J. Oberling, R. J. Oram, B. O’Reilly, C. Osthelder, D. J. Ottaway, H. Overmier, J. R. Palamos, W. Parker, E. Payne, A. Pele, C. J. Perez, M. Pirello, H. Radkins, K. E. Ramirez, J. W. Richardson, K. Riles, N. A. Robertson, J. G. Rollins, C. L. Romel, J. H. Romie, M. P. Ross, K. Ryan, T. Sadecki, E. J. Sanchez, L. E. Sanchez, T. R. Saravanan, R. L. Savage, D. Schaetzl, R. Schnabel, R. M. S. Schofield, E. Schwartz, D. Sellers, T. J. Shaffer, J. R. Smith, S. Soni, B. Sorazu, A. P. Spencer, K. A. Strain, L. Sun, M. J. Szczepańczyk, M. Thomas, P. Thomas, K. A. Thorne, K. Toland, C. I. Torrie, G. Traylor, A. L. Urban, G. Vajente, G. Valdes, D. C. Vander-Hyde, P. J. Veitch, K. Venkateswara, G. Venugopalan, A. D. Viets, C. Vorvick, M. Wade, J. Warner, B. Weaver, R. Weiss, B. Willke, C. C. Wipf, L. Xiao, H. Yamamoto, M. J. Yap, H. Yu, L. Zhang, M. E. Zucker, J. Zweizig, Quantum-Enhanced Advanced LIGO Detectors in the Era of Gravitational-Wave Astronomy. Phys. Rev. Lett. 123, 231107 (2019).
4
Virgo Collaboration, Increasing the Astrophysical Reach of the Advanced Virgo Detector via the Application of Squeezed Vacuum States of Light. Phys. Rev. Lett. 123, 231108 (2019).
5
ADMX Collaboration, Search for Invisible Axion Dark Matter with the Axion Dark Matter Experiment. Phys. Rev. Lett. 120, 151301 (2018).
6
L. Zhong, S. Al Kenany, K. M. Backes, B. M. Brubaker, S. B. Cahn, G. Carosi, Y. V. Gurevich, W. F. Kindel, S. K. Lamoreaux, K. W. Lehnert, S. M. Lewis, M. Malnou, R. H. Maruyama, D. A. Palken, N. M. Rapidis, J. R. Root, M. Simanovskaia, T. M. Shokair, D. H. Speller, I. Urdinaran, K. A. van Bibber, Results from phase 1 of the HAYSTAC microwave cavity axion experiment. Phys. Rev. D 97, 092001 (2018).
7
M. Malnou, D. A. Palken, B. M. Brubaker, L. R. Vale, G. C. Hilton, K. W. Lehnert, Squeezed Vacuum Used to Accelerate the Search for a Weak Classical Signal. Phys. Rev. X 9, 021023 (2019).
8
K. M. Backes, D. A. Palken, S. A. Kenany, B. M. Brubaker, S. B. Cahn, A. Droster, G. C. Hilton, S. Ghosh, H. Jackson, S. K. Lamoreaux, A. F. Leder, K. W. Lehnert, S. M. Lewis, M. Malnou, R. H. Maruyama, N. M. Rapidis, M. Simanovskaia, S. Singh, D. H. Speller, I. Urdinaran, L. R. Vale, E. C. van Assendelft, K. van Bibber, H. Wang, A quantum enhanced search for dark matter axions. Nature 590, 238–242 (2021).
9
K. C. McCormick, J. Keller, S. C. Burd, D. J. Wineland, A. C. Wilson, D. Leibfried, Quantum-enhanced sensing of a single-ion mechanical oscillator. Nature 572, 86–90 (2019).
10
F. Wolf, C. Shi, J. C. Heip, M. Gessner, L. Pezzè, A. Smerzi, M. Schulte, K. Hammerer, P. O. Schmidt, Motional Fock states for quantum-enhanced amplitude and phase measurements with trapped ions. Nat. Commun. 10, 2929 (2019).
11
S. Schreppler, N. Spethmann, N. Brahms, T. Botter, M. Barrios, D. M. Stamper-Kurn, Optically measuring force near the standard quantum limit. Science 344, 1486–1489 (2014).
12
S. Kolkowitz, A. C. Jayich, Q. P. Unterreithmeier, S. D. Bennett, P. Rabl, J. G. E. Harris, M. D. Lukin, Coherent sensing of a mechanical resonator with a single-spin qubit. Science 335, 1603–1606 (2012).
13
R. D. Delaney, A. P. Reed, R. W. Andrews, K. W. Lehnert, Measurement of Motion beyond the Quantum Limit by Transient Amplification. Phys. Rev. Lett. 123, 183603 (2019).
14
K. A. Gilmore, J. G. Bohnet, B. C. Sawyer, J. W. Britton, J. J. Bollinger, Amplitude Sensing below the Zero-Point Fluctuations with a Two-Dimensional Trapped-Ion Mechanical Oscillator. Phys. Rev. Lett. 118, 263602 (2017).
15
W. Wang, Y. Wu, Y. Ma, W. Cai, L. Hu, X. Mu, Y. Xu, Z.-J. Chen, H. Wang, Y. P. Song, H. Yuan, C.-L. Zou, L.-M. Duan, L. Sun, Heisenberg-limited single-mode quantum metrology in a superconducting circuit. Nat. Commun. 10, 4382 (2019).
16
M. Affolter, K. A. Gilmore, J. E. Jordan, J. J. Bollinger, Phase-coherent sensing of the center-of-mass motion of trapped-ion crystals. Phys. Rev. A 102, 052609 (2020).
17
R. A. Thomas, M. Parniak, C. Østfeldt, C. B. Møller, C. Bærentsen, Y. Tsaturyan, A. Schliesser, J. Appel, E. Zeuthen, E. S. Polzik, Entanglement between distant macroscopic mechanical and spin systems. Nat. Phys. 17, 228–233 (2021).
18
M. S. Turner, Windows on the axion. Phys. Rep. 197, 67–97 (1990).
19
See supplementary materials.
20
C. Hempel, B. P. Lanyon, P. Jurcevic, R. Gerritsma, R. Blatt, C. F. Roos, Entanglement-enhanced detection of single-photon scattering events. Nat. Photonics 7, 630–633 (2013).
21
F. Toscano, D. A. R. Dalvit, L. Davidovich, W. H. Zurek, Sub-Planck phase-space structures and Heisenberg-limited measurements. Phys. Rev. A 73, 023803 (2006).
22
M. Penasa, S. Gerlich, T. Rybarczyk, V. Métillon, M. Brune, J. M. Raimond, S. Haroche, L. Davidovich, I. Dotsenko, Measurement of a microwave field amplitude beyond the standard quantum limit. Phys. Rev. A 94, 022313 (2016).
23
R. J. Lewis-Swan, D. Barberena, J. A. Muniz, J. R. K. Cline, D. Young, J. K. Thompson, A. M. Rey, Protocol for Precise Field Sensing in the Optical Domain with Cold Atoms in a Cavity. Phys. Rev. Lett. 124, 193602 (2020).
24
N. S. Kampel, R. W. Peterson, R. Fischer, P.-L. Yu, K. Cicak, R. W. Simmonds, K. W. Lehnert, C. A. Regal, Improving Broadband Displacement Detection with Quantum Correlations. Phys. Rev. X 7, 021008 (2017).
25
M. Jing, Y. Hu, J. Ma, H. Zhang, L. Zhang, L. Xiao, S. Jia, Atomic superheterodyne receiver based on microwave-dressed Rydberg spectroscopy. Nat. Phys. 16, 911–915 (2020).
26
S. C. Burd, R. Srinivas, J. J. Bollinger, A. C. Wilson, D. J. Wineland, D. Leibfried, D. H. Slichter, D. T. C. Allcock, Quantum amplification of mechanical oscillator motion. Science 364, 1163–1165 (2019).
27
J. J. Bollinger, J. W. Britton, B. C. Sawyer, Simulating Quantum Magnetism with Correlated Non-Neutral Ion Plasmas. in Non-Neutral Plasma Physics VIII, AIP Conf. Proc. 1521 (2013), pp. 200–209.
28
B. C. Sawyer, J. W. Britton, J. J. Bollinger, Spin dephasing as a probe of mode temperature, motional state distributions, and heating rates in a two-dimensional ion crystal. Phys. Rev. A 89, 033408 (2014).
29
J. G. Bohnet, B. C. Sawyer, J. W. Britton, M. L. Wall, A. M. Rey, M. Foss-Feig, J. J. Bollinger, Quantum spin dynamics and entanglement generation with hundreds of trapped ions. Science 352, 1297–1301 (2016).
30
A. Safavi-Naini, R. J. Lewis-Swan, J. G. Bohnet, M. Gärttner, K. A. Gilmore, J. E. Jordan, J. Cohn, J. K. Freericks, A. M. Rey, J. J. Bollinger, Verification of a Many-Ion Simulator of the Dicke Model Through Slow Quenches across a Phase Transition. Phys. Rev. Lett. 121, 040503 (2018).
31
S. L. Braunstein, C. M. Caves, Statistical distance and the geometry of quantum states. Phys. Rev. Lett. 72, 3439–3443 (1994).
32
O. Hosten, R. Krishnakumar, N. J. Engelsen, M. A. Kasevich, Quantum phase magnification. Science 352, 1552–1555 (2016).
33
E. Davis, G. Bentsen, M. Schleier-Smith, Approaching the Heisenberg Limit without Single-Particle Detection. Phys. Rev. Lett. 116, 053601 (2016).
34
S. P. Nolan, S. S. Szigeti, S. A. Haine, Optimal and Robust Quantum Metrology Using Interaction-Based Readouts. Phys. Rev. Lett. 119, 193601 (2017).
35
A. Shankar, C. Tang, M. Affolter, K. Gilmore, D. H. E. Dubin, S. Parker, M. J. Holland, J. J. Bollinger, Broadening of the drumhead-mode spectrum due to in-plane thermal fluctuations of two-dimensional trapped ion crystals in a Penning trap. Phys. Rev. A 102, 053106 (2020).
36
A. Facon, E.-K. Dietsche, D. Grosso, S. Haroche, J.-M. Raimond, M. Brune, S. Gleyzes, A sensitive electrometer based on a Rydberg atom in a Schrödinger-cat state. Nature 535, 262–265 (2016).
37
D. H. Meyer, Z. A. Castillo, K. C. Cox, P. D. Kunz, Assessment of Rydberg atoms for wideband electric field sensing. J. Phys. At. Mol. Opt. Phys. 53, 034001 (2020).
38
E. Jordan, K. A. Gilmore, A. Shankar, A. Safavi-Naini, J. G. Bohnet, M. J. Holland, J. J. Bollinger, Near Ground-State Cooling of Two-Dimensional Trapped-Ion Crystals with More than 100 Ions. Phys. Rev. Lett. 122, 053603 (2019).
39
A. V. Dixit, S. Chakram, K. He, A. Agrawal, R. K. Naik, D. I. Schuster, A. Chou, Searching for Dark Matter with a Superconducting Qubit. Phys. Rev. Lett. 126, 141302 (2021).
40
S. Chaudhuri, P. W. Graham, K. Irwin, J. Mardon, S. Rajendran, Y. Zhao, Radio for hidden-photon dark matter detection. Phys. Rev. D 92, 075012 (2015).
41
J. A. Devlin, M. J. Borchert, S. Erlewein, M. Fleck, J. A. Harrington, B. Latacz, J. Warncke, E. Wursten, M. A. Bohman, A. H. Mooser, C. Smorra, M. Wiesinger, C. Will, K. Blaum, Y. Matsuda, C. Ospelkaus, W. Quint, J. Walz, Y. Yamazaki, S. Ulmer, Constraints on the Coupling between Axionlike Dark Matter and Photons Using an Antiproton Superconducting Tuned Detection Circuit in a Cryogenic Penning Trap. Phys. Rev. Lett. 126, 041301 (2021).
42
C. P. Salemi et al., The search for low-mass axion dark matter with ABRACADABRA-10cm. arXiv 2102.06722 [hep-ex] (12 February 2021).
43
W. M. Itano, J. J. Bollinger, J. N. Tan, B. Jelenković, X. Huang, D. J. Wineland, Bragg diffraction from crystallized ion plasmas. Science 279, 686–689 (1998).
44
A. Mortensen, E. Nielsen, T. Matthey, M. Drewsen, Observation of three-dimensional long-range order in small ion coulomb crystals in an RF trap. Phys. Rev. Lett. 96, 103001 (2006).
45
W. H. Zurek, Sub-Planck structure in phase space and its relevance for quantum decoherence. Nature 412, 712–717 (2001).
46
D. F. Walls, G. J. Milburn, Quantum Optics (Springer, ed. 2, 2008).
47
A. M. Rey, L. Jiang, M. Fleischhauer, E. Demler, M. D. Lukin, Many-body protected entanglement generation in interacting spin systems. Phys. Rev. A 77, 052305 (2008).
48
M. J. Biercuk, H. Uys, A. P. VanDevender, N. Shiga, W. M. Itano, J. J. Bollinger, High-fidelity quantum control using ion crystals in a Penning trap. Quantum Inf. Comput. 9, 920–949 (2009).
49
X.-P. Huang, J. J. Bollinger, T. B. Mitchell, W. M. Itano, D. H. E. Dubin, Precise control of the global rotation of strongly coupled ion plasmas in a Penning trap. Phys. Plasmas 5, 1656–1663 (1998).
50
H. Uys, M. J. Biercuk, A. P. Vandevender, C. Ospelkaus, D. Meiser, R. Ozeri, J. J. Bollinger, Decoherence due to elastic Rayleigh scattering. Phys. Rev. Lett. 105, 200401 (2010).
51
J. W. Britton, B. C. Sawyer, A. C. Keith, C.-C. J. Wang, J. K. Freericks, H. Uys, M. J. Biercuk, J. J. Bollinger, Engineered two-dimensional Ising interactions in a trapped-ion quantum simulator with hundreds of spins. Nature 484, 489–492 (2012).
52
D. Leibfried, B. DeMarco, V. Meyer, D. Lucas, M. Barrett, J. Britton, W. M. Itano, B. Jelenković, C. Langer, T. Rosenband, D. J. Wineland, Experimental demonstration of a robust, high-fidelity geometric two ion-qubit phase gate. Nature 422, 412–415 (2003).
53
M. Brownnutt, M. Kumph, P. Rabl, R. Blatt, Ion-trap measurements of electric-field noise near surfaces. Rev. Mod. Phys. 87, 1419–1482 (2015).
54
Y. Kahn, B. R. Safdi, J. Thaler, Broadband and Resonant Approaches to Axion Dark Matter Detection. Phys. Rev. Lett. 117, 141801 (2016).
55
J. L. Ouellet, C. P. Salemi, J. W. Foster, R. Henning, Z. Bogorad, J. M. Conrad, J. A. Formaggio, Y. Kahn, J. Minervini, A. Radovinsky, N. L. Rodd, B. R. Safdi, J. Thaler, D. Winklehner, L. Winslow, First Results from ABRACADABRA-10 cm: A Search for Sub-μeV Axion Dark Matter. Phys. Rev. Lett. 122, 121802 (2019).
Information & Authors
Information
Published In
Science
Volume 373 • Issue 6555 • 6 August 2021
Pages: 673 - 678
History
Received: 15 March 2021
Accepted: 25 June 2021
Copyright
Copyright © 2021 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works.
This is an article distributed under the terms of the Science Journals Default License.
Authors
Funding Information
http://dx.doi.org/10.13039/100000015U.S. Department of Energy:
http://dx.doi.org/10.13039/100000161National Institute of Standards and Technology:
http://dx.doi.org/10.13039/100000161National Institute of Standards and Technology:
http://dx.doi.org/10.13039/100000181Air Force Office of Scientific Research: FA9550-18-1-0319; FA9550-20-1-0019
http://dx.doi.org/10.13039/100000181Air Force Office of Scientific Research: FA9550-18-1-0319
http://dx.doi.org/10.13039/100000181Air Force Office of Scientific Research: FA9550-20-1-0019
http://dx.doi.org/10.13039/100000183Army Research Office: W911NF-16-1-0576
http://dx.doi.org/10.13039/100000183Army Research Office: W911NF-19-1-0210
http://dx.doi.org/10.13039/100000183Army Research Office: NSF PHY1820885
http://dx.doi.org/10.13039/100000183Army Research Office: NSF JILA-PFC PHY-1734006
http://dx.doi.org/10.13039/100000183Army Research Office: NSF QLCI-2016244
http://dx.doi.org/10.13039/100006132Office of Science:
NSF: PHY1820885; NSF JILA-PFC PHY-1734006; QLCI-2016244
National Quantum Information Science Research Centers:
Quantum Systems Accelerator:
DOE Office of Science HEP QuantISED:
DARPA and Army Research Office: W911NF-16-1-0576
ARO single investigator award: W911NF-19-1-0210
DARPA ONISQ program:
