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

Abstract

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...

Testing Lorentz and CPT invariance with ultracold neutrons

“…, where Φ is the uniform Newtonian potential [29]. In this case, the resulting relativistic Hamiltonian is [26] …”

T 3-Interferometer for atoms

“…In this Appendix we describe the population dynamics [30,31,33] of the two resonant atomic states driven by the Raman laser pulses. For this purpose we consider the interaction between a three-level atom and two laser pulses of the form…”

“…(37), during the time interval t i < t < t f , and with Ω j (t i ) = Ω j (t f ) = 0, is given by the evolution operator [33] …”

“…In the present Appendix we derive the complete quantum state of the atom consisting of the internal states as well as the center-of-mass in the two exit ports of our interferometer following the procedure outlined in Refs. [32,33,53]. The dynamics in our interferometer consists of the following steps:…”

Time dilation in quantum systems and decoherence

“…A similar scenario was also studied in [11]. Both works also addressed the discussion about the interpretation of an experiment with atomic fountains [12], namely whether the Compton frequency can be associated with a physical clock in quantum interferometry [13][14][15][16][17], and showed that this cannot be the case as it would lead to an additional observable effect on the interferometric visibility. While the time dilation analysis used for massive particles does not directly apply to the propagation of light, the generalization of [1] to optical interferometry was studied in [2,18], where the Shapiro delay of a single photon can lead to a phase shift or loss of visibility in a quantum optical interferometer.…”