Inertial and gravitational mass in quantum mechanics

Kajari, E.; Harshman, N. L.; Rasel, Ernst M.; Stenholm, Stig; Süssmann, G.; Schleich, W. P.

doi:10.1007/s00340-010-4085-8

Cited by 58 publications

(76 citation statements)

References 62 publications

(141 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Deeper insight [34] into this surprising phenomenon springs from Wigner phase space [48] and the fact that the Wigner function of the Airy wave packet is again an Airy function.…”

Section: Discussionmentioning

confidence: 99%

T 3-Interferometer for atoms

et al. 2017

Self Cite

View full text Add to dashboard Cite

The quantum mechanical propagator of a massive particle in a linear gravitational potential derived already in 1927 by Earle H. Kennard [2, 3] contains a phase that scales with the third power of the time T during which the particle experiences the corresponding force. Since in conventional atom interferometers the internal atomic states are all exposed to the same acceleration a, this T 3 -phase cancels out and the interferometer phase scales as T 2 . In contrast, by applying an external magnetic field we prepare two different accelerations a 1 and a 2 for two internal states of the atom, which translate themselves into two different cubic phases and the resulting interferometer phase scales as T 3 . We present the theoretical background for, and summarize our progress towards experimentally realizing such a novel atom interferometer.

show abstract

“…Deeper insight [34] into this surprising phenomenon springs from Wigner phase space [48] and the fact that the Wigner function of the Airy wave packet is again an Airy function.…”

Section: Discussionmentioning

confidence: 99%

T 3-Interferometer for atoms

et al. 2017

Self Cite

View full text Add to dashboard Cite

show abstract

“…In appendix B we expand on the semi-classical approach toward the interferometer and provide a connection with the Wentzel-Kramers-Brillouin (WKB)-wave function. Moreover we resolve a small puzzle put forward in [60]. In appendix C we then recall an operator identity crucial for our study of the interferometer.…”

Section: Outline Of Articlementioning

confidence: 91%

“…In the present paper we demonstrate that this decomposition of phases and their interpretation in terms of physical phenomena actually depends on the specific quantum mechanical representation chosen to perform the calculation. In order to bring out this fact most clearly we pursue an approach [60] based on operator algebra. In particular, we show that the phase of the interferometer is a consequence of a product of unitary time evolution operators which with the help of the canonical commutation relations between position and momentum operators reduce to a single c-number phase factor.…”

Section: Introductionmentioning

confidence: 99%

A representation-free description of the Kasevich–Chu interferometer: a resolution of the redshift controversy

2013

View full text Add to dashboard Cite

Motivated by a recent claim by Müller et al (2010 Nature 463 926-9) that an atom interferometer can serve as an atom clock to measure the gravitational redshift with an unprecedented accuracy, we provide a representation-free description of the Kasevich-Chu interferometer based on operator algebra. We use this framework to show that the operator product determining the number of atoms at the exit ports of the interferometer is a c-number phase factor whose phase is the sum of only two phases: one is due to the acceleration of the phases of the laser pulses and the other one is due to the acceleration of the atom. This formulation brings out most clearly that this interferometer is an accelerometer or a gravimeter. Moreover, we point out that in different representations of quantum mechanics such as the position or the momentum representation the phase shift appears as though it originates from different physical phenomena. Due to this representation dependence conclusions concerning an enhanced accuracy derived in a specific representation are unfounded. Appendix B. Semi-classical considerations in phase space 38 Appendix C. Operator identity 40 Appendix D. Time evolution of a momentum state in a linear potential 41 Appendix E. Integration over all paths by method of stationary phase 43 References 47 New Journal of Physics 15 (2013) 013007 (http://www.njp.org/)1.1. At the interface of quantum mechanics and general relativity At the same time, the wave nature of matter has opened a new avenue for precision testing of the foundations of physics. Indeed, matter wave interferometry has come a long way from the original experiment of scattering electrons from a single crystal of nickel by Davisson and Germer [5] via neutron interferometry [6] to electron [7], atom, or molecule interferometers [8]; even large molecules such as C 60 show interference properties [9]. A new era has started with the creation of cold atomic beams and the use of light fields as beam splitters [10, 11] and ultra-cold atoms in the form of Bose-Einstein condensates. Here, new tests of general relativity [12], such as the gravito-magnetic field governing the Lense-Thirring effect [13-15], are now within reach by atom interferometry [16-18]. Since atoms experience gravity, such precision tests require microgravity as provided by the International Space Station, and there is indeed a new drive to put atom interferometers into space [19]. An important step toward this goal is a recent experiment performed at the drop tower in Bremen [20] where a Bose-Einstein condensate was created and measured while in free fall. Similarly, the experiments demonstrating interferometry with laser-cooled atoms on a parabolic flight of a plane [21-23] or with Bose-Einstein condensates at the drop tower [24] provide important stepping stones toward tests of general relativity [25] such as the equivalence principle with the wave nature of matter. In this context we also draw attention to the measurement of the quantized energy levels of a neutron in the gravitational f...

show abstract

“…These include the measurement of gravitationally induced quantum phases by neutron interferometry [2], interference experiments on free-falling Bose-Einstein condensates (BECs) [3], the observation of the quantized energy levels of ultracold neutrons (UCNs) [4], and the realization of gravity-resonance spectroscopy [5], which was recently exploited to search for extra short-range interactions [6,7]. Tests of the equivalence principle in the quantum regime were also proposed [8,9]. Other ongoing experiments aim at measuring the gravitational acceleration of antimatter [10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Chirped-frequency excitation of gravitationally bound ultracold neutrons

et al. 2017

View full text Add to dashboard Cite

Ultracold neutrons confined in the Earth's gravitational field display quantized energy levels that have been observed for over a decade. In recent resonance spectroscopy experiments [T. Jenke et al., Nat. Phys. 7, 468 (2011)], the transition between two such gravitational quantum states was driven by the mechanical oscillation of the plates that confine the neutrons. Here we show that by applying a sinusoidal modulation with slowly varying frequency (chirp), the neutrons can be brought to higher excited states by climbing the energy levels one by one. The proposed experiment should make it possible to observe the quantumclassical transition that occurs at high neutron energies. Furthermore, it provides a technique to realize superpositions of gravitational quantum states, to be used for precision tests of gravity at short distances.

show abstract

Inertial and gravitational mass in quantum mechanics

Cited by 58 publications

References 62 publications

T 3-Interferometer for atoms

T 3-Interferometer for atoms

A representation-free description of the Kasevich–Chu interferometer: a resolution of the redshift controversy

Chirped-frequency excitation of gravitationally bound ultracold neutrons

Contact Info

Product

Resources

About