We discuss the coherent splitting and recombining of a nanoparticle in a mesoscopic “closed-loop” Stern–Gerlach interferometer in which the observable is the spin of a single impurity embedded in the particle. This spin, when interacting with a pulsed magnetic gradient, generates the force on the particle. We calculate the internal decoherence, which arises as the displaced impurity excites internal degrees of freedom (phonons) that may provide WelcherWeg information and preclude interference. We estimate the constraints this decoherence channel puts on future interference experiments with massive objects. We find that for a wide range of masses, forces, and temperatures, phonons do not inhibit Stern–Gerlach interferometry with micro-scale objects. However, phonons do constitute a fundamental limit on the splitting of larger macroscopic objects if the applied force induces phonons.

1.
M. P.
Bronstein
,
Phys. Z. Sowjetunion
9
,
140
(
1936
);
reprinted in
Gen. Relativ. Gravit.
44
,
267
(
2012
).
2.
W.
Marshall
,
C.
Simon
,
R.
Penrose
, and
D.
Bouwmeester
,
Phys. Rev. Lett.
91
,
130401
(
2003
).
3.
R.
Marshman
,
A.
Mazumdar
,
G.
Morley
,
P.
Barker
,
S.
Hoekstra
, and
S.
Bose
,
New J. Phys.
22
,
083012
(
2020
).
4.
C.
Wan
,
M.
Scala
,
G.
Morley
,
A.
Rahman
,
H.
Ulbricht
,
J.
Bateman
,
P.
Barker
,
S.
Bose
, and
M.
Kim
,
Phys. Rev. Lett.
117
,
143003
(
2016
).
5.
C.
Marletto
and
V.
Vedral
,
Phys. Rev. Lett.
119
,
240402
(
2017
).
6.
S.
Bose
 et al.,
Phys. Rev. Lett.
119
,
240401
(
2017
).
7.
R.
Marshman
,
A.
Mazumdar
, and
S.
Bose
,
Phys. Rev. A
101
,
052110
(
2020
).
8.
C.
Marletto
and
V.
Vedral
,
Front. Phys.
8
,
176
(
2020
).
9.
D.
Carney
,
H.
Müller
, and
J.
Taylor
,
PRX Quantum
2
,
030330
(
2021
);
D.
Carney
,
H.
Müller
, and
J.
Taylor
, erratum,
PRX Quantum
3
,
010902
(
2022
).
10.
Oriol Romero-Isart
,
Phys. Rev. A
84
,
052121
(
2011
).
11.
G.
Gasbarri
,
A.
Belenchia
,
M.
Carlesso
,
S.
Donadi
,
A.
Bassi
,
R.
Kaltenbaek
,
M.
Paternostro
, and
H.
Ulbricht
,
Commun. Phys.
4
,
155
(
2021
).
12.
M.
Rademacher
,
J.
Millen
, and
Y. L.
Li
,
Adv. Opt. Technol.
9
,
227
(
2020
).
13.
A.
Rahman
,
A.
Frangeskou
,
M.
Kim
,
S.
Bose
,
G.
Morley
, and
P.
Barker
,
Sci. Rep.
6
,
21633
(
2016
).
14.
A.
Albrecht
,
A.
Retzker
, and
M. B.
Plenio
,
Phys. Rev. A
90
,
033834
(
2014
).
15.
Y.
Fein
,
P.
Geyer
,
P.
Zwick
,
F.
Kiałka
,
S.
Pedalino
,
M.
Mayor
,
S.
Gerlich
, and
M.
Arndt
,
Nat. Phys.
15
,
1242
(
2019
).
16.
A.
Shayeghi
,
P.
Rieser
,
G.
Richter
,
U.
Sezer
,
J. H.
Rodewald
,
P.
Geyer
,
T. J.
Martinez
, and
M.
Arndt
,
Nat. Commun.
11
,
1447
(
2020
).
17.
H.
Pino
,
J.
Prat-Camps
,
K.
Sinha
,
B. P.
Venkatesh
, and
O.
Romero-Isart
,
Quantum Sci. Technol.
3
,
025001
(
2018
).
18.
O.
Romero-Isart
,
New J. Phys.
19
,
123029
(
2017
).
19.
Y.
Margalit
 et al.,
Sci. Adv.
7
,
eabg2879
(
2021
).
20.
Y.
Japha
and
R.
Folman
, arXiv:2202.10535 (
2022
).
21.
M. E.
Trusheim
,
L.
Li
,
A.
Laraoui
,
E. H.
Chen
,
H.
Bakhru
,
T.
Schröder
,
O.
Gaathon
,
C. A.
Meriles
, and
D.
Englund
,
Nano Lett.
14
,
32
(
2014
).
22.
J.
Bateman
,
S.
Nimmrichter
,
K.
Hornberger
, and
H.
Ulbricht
,
Nat. Commun.
5
,
5788
(
2014
).
23.
D. E.
Chang
,
C. A.
Regal
,
S. B.
Papp
,
D. J.
Wilson
,
J.
Ye
,
O.
Painter
,
H. J.
Kimble
, and
P.
Zoller
,
Proc. Natl. Acad. Sci. U.S.A.
107
,
1005
(
2010
).
24.
T. W.
van de Kamp
,
R. J.
Marshman
,
S.
Bose
, and
A.
Mazumdar
,
Phys. Rev. A
102
,
062807
(
2020
).
25.
M.
Schut
,
J.
Tilly
,
R. J.
Marshman
,
S.
Bose
, and
A.
Mazumdar
,
Phys. Rev. A
105
,
032411
(
2022
).
26.
P.
Sonnentag
and
F.
Hasselbach
,
Phys. Rev. Lett.
98
,
200402
(
2007
).
27.
A.
Xuereb
,
H.
Ulbricht
, and
M.
Paternostro
,
Sci. Rep.
3
,
3378
(
2013
).
28.
D.
Hümmer
,
R.
Lampert
,
K.
Kustura
,
P.
Maurer
,
C.
Gonzalez-Ballestero
, and
O.
Romero-Isart
,
Phys. Rev. B
101
,
205416
(
2020
).
29.
C.
Gonzalez-Ballestero
,
D.
Hümmer
,
J.
Gieseler
, and
O.
Romero-Isart
,
Phys. Rev. B
101
,
125404
(
2020
).
30.
C.
Gonzalez-Ballestero
,
J.
Gieseler
, and
O.
Romero-Isart
,
Phys. Rev. Lett.
124
,
093602
(
2020
).
31.
M.
Strungaru
,
M. O. A.
Ellis
,
S.
Ruta
,
O.
Chubykalo-Fesenko
,
R. F. L.
Evans
, and
R. W.
Chantrell
,
Phys. Rev. B
103
,
024429
(
2021
).
32.
J. S.
Pedernales
,
G. W.
Morley
, and
M. B.
Plenio
,
Phys. Rev. Lett.
125
,
023602
(
2020
).
33.
R. J.
Marshman
,
A.
Mazumdar
,
R.
Folman
, and
S.
Bose
,
Phys. Rev. Res.
4
,
023087
(
2022
).
34.
We checked that in the limit q0, one recovers the center-of-mass dynamics of Eq. (4).
35.
36.
A. C.
Levi
and
H.
Suhl
,
Surf. Sci.
88
,
221
(
1979
).
37.
Zero-Phonon Lines and Spectral Hole Burning in Spectroscopy and Photochemistry
, edited by
O.
Sild
and
K.
Haller
(
Springer
,
1988
).
38.
D.
Hsu
and
J. L.
Skinner
,
J. Chem. Phys.
81
,
1604
(
1984
).
39.
W. P.
Schleich
,
Quantum Optics in Phase Space
(
Wiley-VCH
,
Berlin
,
2001
).
40.
W.
Vogel
,
D.-G.
Welsch
, and
S.
Wallentowitz
,
Quantum Optics: An Introduction
(
Wiley-VCH
,
Berlin, Weinheim
,
2001
).
41.
P. W.
Milonni
,
The Quantum Vacuum
(
Academic
,
San Diego
,
1994
).
42.
O. M.
Friesch
,
I.
Marzoli
, and
W. P.
Schleich
,
New J. Phys.
2
,
004
(
2000
).
43.
K.
Bongs
,
R.
Launay
, and
M.
Kasevich
,
Appl. Phys. B
84
,
599
(
2006
).
44.
O.
Amit
, “
Matter-wave interferometry on an atom chip
,” Ph.D. thesis (Ben-Gurion University of the Negev, Beer Sheva,
2020
).
45.
U.
Delić
,
M.
Reisenbauer
,
K.
Dare
,
D.
Grass
,
V.
Vuletić
,
N.
Kiesel
, and
M.
Aspelmeyer
,
Science
367
,
892
(
2020
).
46.
F.
Tebbenjohanns
,
M.
Frimmer
,
V.
Jain
,
D.
Windey
, and
L.
Novotny
,
Phys. Rev. Lett.
124
,
013603
(
2020
).
47.
F.
Tebbenjohanns
,
M. L.
Mattana
,
M.
Rossi
,
M.
Frimmer
, and
L.
Novotny
,
Nature
595
,
378
(
2021
).
48.
L.
Magrini
,
P.
Rosenzweig
,
C.
Bach
,
A.
Deutschmann-Olek
,
S. G.
Hofer
,
S.
Hong
,
N.
Kiesel
,
A.
Kugi
, and
M.
Aspelmeyer
,
Nature
595
,
373
(
2021
).
50.
N. G.
van Kampen
,
J. Stat. Phys.
78
,
299
(
1995
).
51.
G. M.
Palma
,
K.-A.
Suominen
, and
A. K.
Ekert
,
Proc. R. Soc. London, Ser. A
452
,
567
(
1996
).
52.
Y.
Romach
 et al.,
Phys. Rev. Lett.
114
,
017601
(
2015
).
53.
E. D.
Herbschleb
et al.,
Nat. Commun.
10
,
3766
(
2019
).
54.
N.
Bar-Gill
,
L.
Pham
,
A.
Jarmola
,
D.
Budker
, and
R.
Walsworth
,
Nat. Commun.
4
,
1743
(
2013
).
55.
A.
Waxman
,
H.
Schlussel
,
D.
Groswasser
,
V. M.
Acosta
,
L.-S.
Bouchard
,
D.
Budker
, and
R.
Folman
,
Phys. Rev. B
89
,
054509
(
2014
).
56.
Y.
Schlussel
et al.,
Phys. Rev. Appl.
10
,
034032
(
2018
).
57.
Y.
Rosenzweig
,
Y.
Schlussel
, and
R.
Folman
,
Phys. Rev. B
98
,
014112
(
2018
).
58.
E.
Duval
,
L.
Saviot
,
A.
Mermet
, and
D. B.
Murray
,
J. Phys. Condens. Matt.
17
,
3559
(
2005
).
59.
W. H.
Zurek
,
Phys. Today
44
(
10
),
36
(
1991
).
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