Abstract
We have produced a phase modulation of a matter wave by applying a time-dependent perturbation. In the present study, the perturbation is the Stark effect produced by an electric field and, as this effect is quadratic in the applied field, this is the atom optics equivalent of the Kerr effect. In the present paper, we first develop an exact theory of phase modulation and we find results in agreement with a semiclassical calculation assuming a localized wavepacket. We then describe briefly our experimental setup which uses an atom interferometer to detect the phase modulations produced on its two arms which are spatially separated. The interferometer signal exhibits periodic oscillations, at the frequency of the modulation and its harmonics, when the same modulation frequency is applied on the two arms, and at the difference frequency and its harmonics when two different frequencies are used. All the experimental results are in very good agreement with theory.
Graphical abstract
Similar content being viewed by others
References
Ch.J. Bordé, in Atom interferometry, edited by P.R. Berman (Academic Press, San Diego, CA, 1997), p. 257
H. Rauch, S. Werner, in Neutron interferometry, Oxford series on neutron scattering in condensed matter (Clarendon Press, Oxford, 2000), Vol. 12
A.D. Cronin, J. Schmiedmayer, D.E. Pritchard, Rev. Mod. Phys. 81, 1052 (2009)
Atom interferometry, in Proceedings of the International School of Physics “Enrico Fermi”, edited by G.M. Tino, M.A. Kasevich (Società Italian di Fisica, Bologne, Italy, 2014)
F. Hasselbach, Rep. Prog. Phys. 73, 016101 (2010)
M. Moshinsky, Phys. Rev. 88, 625 (1952)
J. Felber, G. Müller, R. Gähler, R. Golub, Physica B 162, 191 (1990)
Č. Brukner, A. Zeilinger, Phys. Rev. A 56, 3804 (1997)
A. del Campo, G. Garca-Calderón, J. Muga, Phys. Rep. 476, 1 (2009)
E. Torrontegui, J. Muñoz, Y. Ban, J.G. Muga, Phys. Rev. A 83, 043608 (2011)
W.A. Hamilton, A.G. Klein, G.I. Opat, P.A. Timmins, Phys. Rev. Lett. 58, 2770 (1987)
A. Steane, P. Szriftgiser, P. Desbiolles, J. Dalibard, Phys. Rev. Lett. 74, 4972 (1995)
P. Szriftgiser, D. Guéry-Odelin, M. Arndt, J. Dalibard, Phys. Rev. Lett. 77, 4 (1996)
Y. Colombe, B. Mercier, H. Pérrin, V. Lorent, Phys. Rev. A 72, 061601(R) (2005)
J. Felber, R. Gälher, C. Rausch, R. Golub, Phys. Rev. A 53, 319 (1996)
A.I. Frank et al., Phys. Lett. A 311, 6 (2003)
A.I. Frank et al., Nucl. Instrum. Methods Phys. Res. A 611, 314 (2009)
I. Bloch, T.W. Hänsch, T. Esslinger, Nature 403, 166 (2000)
T.D. Roberts, A.D. Cronin, M.V. Tiberg, D.E. Pritchard, Phys. Rev. Lett. 92, 060405 (2004)
W.F. Holmgren, I. Hromada, C.E. Klauss, A.D. Cronin, New. J. Phys. 13, 115007 (2011)
E.T. Smith et al., Phys. Rev. Lett. 81, 1996 (1998)
R.A. Rubenstein et al., Phys. Rev. Lett. 82, 2018 (1999)
S. Bernet et al., Phys. Rev. Lett. 77, 5160 (1996)
S. Bernet et al., Phys. Rev. A 62, 023606 (2000)
B. Decamps, J. Gillot, A. Gauguet, J. Vigué, M. Büchner, Phys. Rev. Lett. 116, 053004 (2016)
P. Storey, C. Cohen-Tannoudji, J. Phys. II 4, 1999 (1994)
W. Li, L.E. Reichl, Phys. Rev. B 60, 15732 (1999)
P.A. Martin, J. Phys. A: Math. Theor. 41, 015207 (2008)
Digital Library of Mathematical Functions, equation 10.23.6 and 10.23.7, http://dlmf.nist.gov/10.23
H.T. Koelink, R.F. Swarttouw, J. Approx. Theory 87, 260 (1995)
F. Pockels, Ueber den Einfluss des elektrostatischen Feldes auf das optische Verhalten piëzoelektrischer Krystalle, (Abhandlungen der mathematisch-physikalischen Klasse der Königlichen Gesellschaft der Wissenschaften zu Göttingen), Band 39 (1893)
J. Kerr, Philos. Mag. Ser. 4 50, 337 (1875)
M.-A. Bouchiat, C. Bouchiat, Rep. Prog. Phys. 60, 1351 (1997)
The ACME Collaboration, Science 343, 269 (2014)
T. Fleig, M.N. Nayak, J. Mol. Spectrosc. 300, 16 (2014)
Z. Bialynicka-Birula, I. Bialynicka-Birula, Phys. Rev. D 2, 2341 (1970)
H. Euler, B. Kockel, Naturwissenschaften 23, 246 (1935)
A. Miffre, M. Jacquey, M. Büchner, G. Trénec, J. Vigué, Eur. Phys. J. D 33, 99 (2005)
A. Miffre, PhD thesis, Université P. Sabatier, 2011, http://tel.archives-ouvertes.fr/
S. Lepoutre, PhD thesis, Université P. Sabatier, 2011, http://tel.archives-ouvertes.fr/
J.P. Toennies, K. Winkelmann, J. Chem. Phys. 66, 3965 (1977)
D.R. Miller, in Atomic and molecular beam methods, edited by G. Scoles (Oxford University Press, Oxford, 1988)
M. Jacquey, A. Miffre, M. Büchner, G. Trénec, J. Vigué, Europhys. Lett. 77, 20007 (2007)
R. Delhuille, A. Miffre, E. Lavallette, M. Büchner, C. Rizzo, G. Trénec, J. Vigué, H.J. Loesch, J.P. Gauyacq, Rev. Sci. Instrum. 73, 2249 (2002)
S. Lepoutre, V.P.A. Lonij, H. Jelassi, G. Trénec, M. Büchner, A.D. Cronin, J. Vigué, Eur. Phys. J. D 62, 309 (2011)
S. Lepoutre, A. Gauguet, G. Trénec, M. Büchner, J. Vigué, Phys. Rev. Lett. 109, 120404 (2012)
J. Gillot, S. Lepoutre, A. Gauguet, M. Büchner, J. Vigué, Phys. Rev. Lett. 111, 030401 (2013)
S. Lepoutre, J. Gillot, A. Gauguet, G. Trénec, M. Büchner, J. Vigué, Phys. Rev. A 88, 043628 (2013)
M.S. Sorem, A.L. Schawlow, Opt. Commun. 5, 148 (1972)
G.N. Watson, A treatise on the theory of Bessel functions (Cambridge Mathematical Library, Cambridge, 1995)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Décamps, B., Gillot, J., Gauguet, A. et al. Phase modulation of atom waves: theory and experiment using the atom optics analogue of the Kerr effect. Eur. Phys. J. D 71, 334 (2017). https://doi.org/10.1140/epjd/e2017-80616-5
Received:
Published:
DOI: https://doi.org/10.1140/epjd/e2017-80616-5