Atom interferometer

Short description: Interferometer which uses the wave-like nature of atoms

An atom interferometer uses the wave-like nature of atoms in order to produce interference. In atom interferometers, the roles of matter and light are reversed compared to the laser based interferometers, i.e. the beam splitter and mirrors are lasers while the source emits matter waves (the atoms) rather than light. In this sense, atom interferometers are the matter wave analog of double-slit, Michelson-Morley, or Mach-Zehnder interferometers typically used for light.[1] Atom interferometers measure the difference in phase acquired by atomic matter waves traversing different paths. Matter waves may be controlled and manipulated using systems of lasers.[2]: 420–1 Atom interferometers have been used in tests of fundamental physics, including measurements of the gravitational constant, the fine-structure constant, and universality of free fall. Applied uses of atom interferometers include accelerometers, rotation sensors, and gravity gradiometers.[3]

## Contents

* 1 Overview
* 2 History
* 3 Interferometer types
* 3.1 Light pulse atom interferometer
* 4 Examples
* 5 Applications
* 5.1 Gravitational physics
* 5.2 Inertial navigation
* 6 See also
* 7 References
* 8 External links

## Overview

Interferometry splits a wave into a superposition along two different paths. A spatially dependent potential or a local interaction differentiates the paths, introducing a phase difference between waves. Atom interferometers use center of mass matter waves with short de Broglie wavelength.[4] [5] Experiments using molecules have been proposed to search for the limits of quantum mechanics by leveraging the molecules' shorter De Broglie wavelengths.[6]

## History

Interference of atom matter waves was first observed by Immanuel Estermann and Otto Stern in 1930, when a sodium (Na) beam was diffracted off a surface of sodium chloride (NaCl).[7] The first modern atom interferometer reported was a double-slit experiment with metastable helium atoms and a microfabricated double slit by O. Carnal and Jürgen Mlynek in 1991,[8] and an interferometer using three microfabricated diffraction gratings and Na atoms in the group around David E. Pritchard at the Massachusetts Institute of Technology (MIT).[9] Shortly afterwards, an optical version of a Ramsey spectrometer typically used in atomic clocks was recognized also as an atom interferometer at the Physikalisch-Technische Bundesanstalt (PTB) in Braunschweig, Germany.[10] The largest physical separation between the partial wave packets of atoms was achieved using laser cooling techniques and stimulated Raman transitions by Steven Chu and his coworkers in Stanford University.[11]

In 1999, the diffraction of C60 fullerenes by researchers from the University of Vienna was reported.[12] Fullerenes are comparatively large and massive objects, having an atomic mass of about 720 Da. The de Broglie wavelength of the incident beam was about 2.5 pm, whereas the diameter of the molecule is about 1 nm, about 400 times larger. In 2012, these far-field diffraction experiments could be extended to phthalocyanine molecules and their heavier derivatives, which are composed of 58 and 114 atoms respectively. In these experiments the build-up of such interference patterns could be recorded in real time and with single molecule sensitivity.[13]

In 2003, the Vienna group also demonstrated the wave nature of tetraphenylporphyrin[14]—a flat biodye with an extension of about 2 nm and a mass of 614 Da. For this demonstration they employed a near-field Talbot–Lau interferometer.[15][16] In the same interferometer they also found interference fringes for C60F48, a fluorinated buckyball with a mass of about 1600 Da, composed of 108 atoms.[14] Large molecules are already so complex that they give experimental access to some aspects of the quantum-classical interface, i.e., to certain decoherence mechanisms.[17][18] In 2011, the interference of molecules as heavy as 6910 Da could be demonstrated in a Kapitza–Dirac–Talbot–Lau interferometer.[19] In 2013, the interference of molecules beyond 10,000 Da has been demonstrated.[20]

The 2008 comprehensive review by Alexander D. Cronin, Jörg Schmiedmayer, and David E. Pritchard documents many new experimental approaches to atom interferometry.[21] More recently atom interferometers have begun moving out of laboratory conditions and have begun to address a variety of applications in real world environments.[22][23]

## Interferometer types

A compact Magneto-optical Trap, the first step in generating an atom interferometer.

While the use of atoms offers easy access to higher frequencies (and thus accuracies) than light, atoms possess mass and move slower; thus they affected more noticeably by gravity compared to beams of light.[24] In some apparatuses, the atoms are ejected upwards and the interferometry takes place while the atoms are in flight, or while falling in free flight.[25] In other experiments gravitational effects by free acceleration are not negated; additional forces are used to compensate for gravity.[26][27] These guided systems in principle can provide arbitrary amounts of measurement time, provided quantum coherence is preserved.

The early atom interferometers deployed slits or wires for the beam splitters and mirrors. Later systems, especially the guided ones, used light forces for splitting and reflecting of the matter wave.[28]

### Light pulse atom interferometer

A prototypical technique for atom interferometry involves splitting, reflecting, and recombining atomic matter waves using pulses of light. This technique is also called the Kasevich-Chu atom interferometer, named after the authors of the 1991 paper.[29] This method employs counter-propagating beams of light that produce transitions between two quantum states labeled |0⟩ and |1⟩.[30] Both lasers are tuned off-resonance from the excited state by a frequency Δ to avoid resonantly exciting and heating the atoms.

In addition to changing the spin state of the atom, the counter-propagating Raman transition provides a momentum kick ℏk→eff=ℏ(k→2−k→1) to one of the components.[30] In a spin–momentum basis, a pulse of Raman light interacting with an atom will transition between |0,0⟩ and |1,ℏk→eff⟩. Applying a π/2 pulse (see Ramsey interferometer) light to ψ0=|0,0⟩ produces the entangled state ψ1=12(|0,0⟩+|1,ℏk→eff⟩).

The interferometer is formed by three Raman pulses in a π/2–π–π/2 configuration separated by a common non-interaction time T. This scheme is analogous to a Mach–Zehnder interferometer for light, where the first pulse splits the matter wave to travel along two different trajectories, the second pulse reflects the packets back toward each other, and the final pulse recombines the matter wave. The measured state of the matter wave after the interferometer sequence depends on the total phase difference Δφ accumulated along the two different trajectories, yielding a final probability of being in one of the states as[31]P=12(1−Ccos⁡(Δφ)),where C is the visibility or contrast of the interferometer fringe. Since the matter wave is in free-fall with respect to gravity, the phase difference depends on the gravitational acceleration g as[30]Δφ=k→eff⋅g→T2+ΔϕL,where ΔϕL is any additional phase difference of the Raman laser beam arising between the light pulses.[32]

The sensitivity of the interferometer to gravitational or inertial forces depends on:

* The space–time area enclosed by the interferometer, which increases for larger T.[33]
* The relative phase stability of the counter-propagating Raman beams.
* The number of atoms in the cold, trapped ensemble that complete the interferometer. A larger fraction of participating atoms increases C. Due to the Doppler effect, atoms with finite temperature may not experience exactly π/2 or π Raman pulses.

## Examples

Group  | Year  | Atomic species  | Method  | Measured effect(s)

|
|
|
|

Pritchard | 1991  | Na, Na2 | Nano-fabricated gratings | Polarizability, index of refraction
Clauser  | 1994  | K | Talbot–Lau interferometer  |
Zeilinger  | 1995  | Ar | Standing light wave diffraction gratings  |
Helmke
Bordé  | 1991  |  | Ramsey–Bordé | Polarizability,
Aharonov–Bohm effect: exp/theo 0.99±0.022,
Sagnac effect 0.3 rad/s/√Hz
Chu  | 1991
1998  | Na

| Kasevich–Chu interferometer
Light pulses Raman diffraction  | Gravimeter: 3⋅10−10
Fine-structure constant: α±1.5⋅10−9
Kasevich  | 1997
1998  | Cs  | Light pulses Raman diffraction  | Gyroscope: 2⋅10−8rad/s/√Hz,
Gradiometer:
Berman  |  |  | Talbot-Lau  |
Mueller  | 2018  | Cs  | Ramsey-Bordé interferometer  | Fine-structure constant: α±2⋅10−10

## Applications

### Gravitational physics

A precise measurement of gravitational redshift was made in 2009 by Holger Muller, Achim Peters, and Steven Chu. No violations of general relativity were found to 7×10−9.[34]

In 2020, Peter Asenbaum, Chris Overstreet, Minjeong Kim, Joseph Curti, and Mark A. Kasevich used atom interferometry to test the principle of equivalence in general relativity. They found no violations to about 10−12.[35][36]

The sensitivity of an atom interferometer to external influences generally improves as the mater wave's separation time increases.[34] High sensitivity free-fall interferometers hence require long drop distances. For example, the MAGIS-100 experiment at Fermilab employs a 100 meter drop tower, aiming to detect gravitational waves and ultralight dark matter,[37] which is known to interact with regular matter only via gravity.

Space-based atom interferometers may be more sensitive to weak gravitational waves than terrestrial observatories such as LIGO.[38]

### Inertial navigation

Atomic interferometer gyroscopes (AIG) and atomic spin gyroscopes (ASG) use atomic interferometer to sense rotation or in the latter case, uses atomic spin to sense rotation with both having compact size, high precision, and the possibility of being made on a chip-scale.[39][40]

## See also

* Electron interferometer
* Ramsey interferometry

## References

1. ↑ Cronin, Alexander D.; Schmiedmayer, Jörg; Pritchard, David E. (2009-07-28). "Optics and interferometry with atoms and molecules". Reviews of Modern Physics 81 (3): 1051–1129. doi:10.1103/RevModPhys.81.1051. Bibcode: 2009RvMP...81.1051C. https://link.aps.org/doi/10.1103/RevModPhys.81.1051.
2. ↑ Hecht, Eugene (2017). Optics (5th ed.). Pearson. ISBN 978-0-133-97722-6.
3. ↑ Stray, Ben; Lamb, Andrew; Kaushik, Aisha; Vovrosh, Jamie; Winch, Jonathan; Hayati, Farzad; Boddice, Daniel; Stabrawa, Artur et al. (2020). "Quantum sensing for gravity cartography". Nature 602 (7898): 590–594. doi:10.1038/s41586-021-04315-3. PMID 35197616.
4. ↑ Cronin, A. D.; Schmiedmayer, J.; Pritchard, D. E. (2009). "Optics and interferometry with atoms and molecules". Rev. Mod. Phys. 81 (3): 1051–1129. doi:10.1103/RevModPhys.81.1051. Bibcode: 2009RvMP...81.1051C.
5. ↑ Adams, C. S.; Sigel, M.; Mlynek, J. (1994). "Atom Optics". Phys. Rep. 240 (3): 143–210. doi:10.1016/0370-1573(94)90066-3. Bibcode: 1994PhR...240..143A.
6. ↑ Hornberger, K. (2012). "Colloquium: Quantum interference of clusters and molecules". Rev. Mod. Phys. 84 (1): 157. doi:10.1103/revmodphys.84.157. Bibcode: 2012RvMP...84..157H.
7. ↑ Estermann, I.; Stern, Otto (1930). "Beugung von Molekularstrahlen". Z. Phys. 61 (1–2): 95. doi:10.1007/bf01340293. Bibcode: 1930ZPhy...61...95E.
8. ↑ Carnal, O.; Mlynek, J. (1991). "Young's double-slit experiment with atoms: A simple atom interferometer". Phys. Rev. Lett. 66 (21): 2689–2692. doi:10.1103/physrevlett.66.2689. PMID 10043591. Bibcode: 1991PhRvL..66.2689C. http://elib.bsu.by/handle/123456789/154548.
9. ↑ Keith, D.W.; Ekstrom, C.R.; Turchette, Q.A.; Pritchard, D.E. (1991). "An interferometer for atoms". Phys. Rev. Lett. 66 (21): 2693–2696. doi:10.1103/physrevlett.66.2693. PMID 10043592. Bibcode: 1991PhRvL..66.2693K. http://elib.bsu.by/handle/123456789/154551.
10. ↑ Riehle, F.; Th; Witte, A.; Helmcke, J.; Ch; Bordé, J. (1991). "Optical Ramsey spectroscopy in a rotating frame: Sagnac effect in a matter-wave interferometer". Phys. Rev. Lett. 67 (2): 177–180. doi:10.1103/physrevlett.67.177. PMID 10044514. Bibcode: 1991PhRvL..67..177R.
11. ↑ Kasevich, M.; Chu, S. (1991). "Atomic interferometry using stimulated Raman transitions". Phys. Rev. Lett. 67 (2): 181–184. doi:10.1103/physrevlett.67.181. PMID 10044515. Bibcode: 1991PhRvL..67..181K.
12. ↑ Arndt, Markus; O. Nairz; J. Voss-Andreae, C. Keller, G. van der Zouw, A. Zeilinger (14 October 1999). "Wave–particle duality of C60". Nature 401 (6754): 680–682. doi:10.1038/44348. PMID 18494170. Bibcode: 1999Natur.401..680A.
13. ↑ Juffmann, Thomas (25 March 2012). "Real-time single-molecule imaging of quantum interference". Nature Nanotechnology 7 (5): 297–300. doi:10.1038/nnano.2012.34. PMID 22447163. Bibcode: 2012NatNa...7..297J.
14. ↑ 14.0 14.1 Hackermüller, Lucia; Stefan Uttenthaler; Klaus Hornberger; Elisabeth Reiger; Björn Brezger; Anton Zeilinger; Markus Arndt (2003). "The wave nature of biomolecules and fluorofullerenes". Phys. Rev. Lett. 91 (9). doi:10.1103/PhysRevLett.91.090408. PMID 14525169. Bibcode: 2003PhRvL..91i0408H.
15. ↑ Clauser, John F.; S. Li (1994). "Talbot von Lau interefometry with cold slow potassium atoms.". Phys. Rev. A 49 (4): R2213–2217. doi:10.1103/PhysRevA.49.R2213. PMID 9910609. Bibcode: 1994PhRvA..49.2213C.
16. ↑ Brezger, Björn; Lucia Hackermüller; Stefan Uttenthaler; Julia Petschinka; Markus Arndt; Anton Zeilinger (2002). "Matter-wave interferometer for large molecules". Phys. Rev. Lett. 88 (10). doi:10.1103/PhysRevLett.88.100404. PMID 11909334. Bibcode: 2002PhRvL..88j0404B.
17. ↑ Hornberger, Klaus; Stefan Uttenthaler; Björn Brezger; Lucia Hackermüller; Markus Arndt; Anton Zeilinger (2003). "Observation of Collisional Decoherence in Interferometry". Phys. Rev. Lett. 90 (16). doi:10.1103/PhysRevLett.90.160401. PMID 12731960. Bibcode: 2003PhRvL..90p0401H.
18. ↑ Hackermüller, Lucia; Klaus Hornberger; Björn Brezger; Anton Zeilinger; Markus Arndt (2004). "Decoherence of matter waves by thermal emission of radiation". Nature 427 (6976): 711–714. doi:10.1038/nature02276. PMID 14973478. Bibcode: 2004Natur.427..711H.
19. ↑ Gerlich, Stefan (2011). "Quantum interference of large organic molecules". Nature Communications 2 (263). doi:10.1038/ncomms1263. PMID 21468015. Bibcode: 2011NatCo...2..263G.
20. ↑ Eibenberger, S.; Gerlich, S.; Arndt, M.; Mayor, M.; Tüxen, J. (2013). "Matter–wave interference of particles selected from a molecular library with masses exceeding 10 000 amu". Physical Chemistry Chemical Physics 15 (35): 14696–14700. doi:10.1039/c3cp51500a. PMID 23900710. Bibcode: 2013PCCP...1514696E.
21. ↑ Cronin, Alexander D.; Schmiedmayer, Jörg; Pritchard, David E. (2009). "Optics and interferometry with atoms and molecules". Reviews of Modern Physics 81 (3): 1051–1129. doi:10.1103/RevModPhys.81.1051. Bibcode: 2009RvMP...81.1051C.
22. ↑ Bongs, K.; Holynski, M.; Vovrosh, J.; Bouyer, P.; Condon, G.; Rasel, E.; Schubert, C.; Schleich, W.P. et al. (2019). "Taking atom interferometric quantum sensors from the laboratory to real-world applications". Nat. Rev. Phys. 1 (12): 731–739. doi:10.1038/s42254-019-0117-4. Bibcode: 2019NatRP...1..731B.
23. ↑ Vovrosh, J.; Dragomir, A.; Stray, B.; Boddice, B. (2023). "Advances in Portable Atom Interferometry-Based Gravity Sensing". Sensors 23 (7): 7651. doi:10.3390/s23177651. PMID 37688106. Bibcode: 2023Senso..23.7651V.
24. ↑ Lindley, David (2005-07-12). "The Weight of Light" (in en). Physics 16: 1. doi:10.1103/PhysRevLett.4.337. https://physics.aps.org/story/v16/st1.
25. ↑ Peters, Achim; Chung, Keng Yeow; Chu, Steven (August 1999). "Measurement of gravitational acceleration by dropping atoms" (in en). Nature 400 (6747): 849–852. doi:10.1038/23655. ISSN 1476-4687. Bibcode: 1999Natur.400..849P. https://www.nature.com/articles/23655.
26. ↑ Wu, Saijun; Su, Edward; Prentiss, Mara (2007-10-25). "Demonstration of an Area-Enclosing Guided-Atom Interferometer for Rotation Sensing". Physical Review Letters 99 (17). doi:10.1103/PhysRevLett.99.173201. PMID 17995327. Bibcode: 2007PhRvL..99q3201W. https://link.aps.org/doi/10.1103/PhysRevLett.99.173201.
27. ↑ McDonald, G. D.; Keal, H.; Altin, P. A.; Debs, J. E.; Bennetts, S.; Kuhn, C. C. N.; Hardman, K. S.; Johnsson, M. T. et al. (2013-01-28). "Optically guided linear Mach-Zehnder atom interferometer". Physical Review A 87 (1). doi:10.1103/PhysRevA.87.013632. Bibcode: 2013PhRvA..87a3632M. https://link.aps.org/doi/10.1103/PhysRevA.87.013632.
28. ↑ Rasel, E. M. (1995). "Atom Wave Interferometry with Diffraction Gratings of Light". Phys. Rev. Lett. 75 (14): 2633–2637. doi:10.1103/physrevlett.75.2633. PMID 10059366. Bibcode: 1995PhRvL..75.2633R. http://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1006&context=physicsbatelaan.
29. ↑ Kasevich, Mark; Chu, Steven (1991-07-08). "Atomic interferometry using stimulated Raman transitions". Physical Review Letters 67 (2): 181–184. doi:10.1103/PhysRevLett.67.181. PMID 10044515. Bibcode: 1991PhRvL..67..181K. https://link.aps.org/doi/10.1103/PhysRevLett.67.181.
30. ↑ 30.0 30.1 30.2 Sorrentino, F.; Angelis, M. de; Bertoldi, A.; Cacciapuoti, L.; Giorgini, A.; Prevedelli, M.; Rosi, G.; Tino, G. M. (2009). "Precision measurements of gravity using cold atom sensors" (in en). Journal of the European Optical Society: Rapid Publications 4: 09025. doi:10.2971/jeos.2009.09025. ISSN 1990-2573. Bibcode: 2009JEOS....4E9025S. https://jeos.edpsciences.org/articles/jeos/abs/2009/01/jeos20090409025/jeos20090409025.html.
31. ↑ "Optica Publishing Group". https://opg.optica.org/oe/viewmedia.cfm?uri=oe-32-24-42856&html=true.
32. ↑ HosseiniArani, Alireza; Schilling, Manuel; Beaufils, Quentin; Knabe, Annike; Tennstedt, Benjamin; Kupriyanov, Alexey; Schön, Steffen; Pereira dos Santos, Franck et al. (2024-10-01). "Advances in Atom Interferometry and their Impacts on the Performance of Quantum Accelerometers On-board Future Satellite Gravity Missions". Advances in Space Research 74 (7): 3186–3200. doi:10.1016/j.asr.2024.06.055. ISSN 0273-1177. Bibcode: 2024AdSpR..74.3186H. https://www.sciencedirect.com/science/article/pii/S027311772400646X.
33. ↑ Arndt, Markus (2013-02-25). "Free-Falling Interferometry" (in en). Physics 6 (9): 23. doi:10.1103/PhysRevLett.110.093602. PMID 23496709. https://physics.aps.org/articles/v6/23.
34. ↑ 34.0 34.1 Muller, Holger; Peters, Achim; Chu, Steven (2010). "A precision measurement of the gravitational redshift by the interference of matter waves". Nature 463 (7283): 926–929. doi:10.1038/nature08776. PMID 20164925. Bibcode: 2010Natur.463..926M. https://www.nature.com/articles/nature08776.
35. ↑ Asenbaum, Peter; Overstreet, Chris; Kim, Minjeong; Curti, Joseph; Kasevich, Mark A. (2020). "Atom-Interferometric Test of the Equivalence Principle at the 10−12 Level". Physical Review Letters 125 (19). doi:10.1103/PhysRevLett.125.191101. PMID 33216577. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.125.191101.
36. ↑ Conover, Emily (October 28, 2020). "Galileo's famous gravity experiment holds up, even with individual atoms". Science News. https://www.sciencenews.org/article/galileo-gravity-experiment-atoms-general-relativity-einstein.
37. ↑ "Outline" (in en-US). https://magis.fnal.gov/.
38. ↑ Andersen, Ross D. (2013-10-01). "Gravitational Wave Detectors Get Ready to Hunt for the Big Bang" (in en). https://www.scientificamerican.com/article/gravitational-wave-detectors-get-ready-to-hunt-for-the-big-bang/.
39. ↑ Fang, Jiancheng; Qin, Jie (2012). "Advances in Atomic Gyroscopes: A View from Inertial Navigation Applications". Sensors 12 (5): 6331–6346. doi:10.3390/s120506331. PMID 22778644. Bibcode: 2012Senso..12.6331F.
40. ↑ Advances in Atomic Gyroscopes: A View from Inertial Navigation Applications. Full PDF

## External links

* P. R. Berman [Editor], Atom Interferometry. Academic Press (1997). Detailed overview of atom interferometers at that time (good introductions and theory).
* Stedman Review of the Sagnac Effect

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