Session R02: Advances in Atom Interferometry

Theoretical Description of Beamsplitters and Mirrors in Potentials via Oscillator Equations

Atom interferometry has shown to be very successful in a myriad of applications including its use for sensing gravity [1], magnetic fields and its gradients [2], and has shown potential to detect dark matter [3, 4]. Recently the focus has shifted towards improving the sensitivity to reach an accuracy beyond the standard quantum limit [5]. In order to keep the Bose-Einstein-Condensate (BEC) entangled over the interferometer sequence, experiments have shown that beam splitters and mirrors need to reach a high level of efficiency [6]. Therefore an in-depth study of the underlying diffraction process in beam splitters and mirrors is crucial for performing interferometry where the BEC’s external degrees of freedom are entangled.

Here, we provide an approach for the theoretical modeling of the diffraction process by considering operator-valued oscillation equations for arbitrary trapping potentials. We provide explicit, non-trivial examples that can be solved in a straight-forward manner with our method.

[1] Phys. Rev. A 88, 043610 (2013).

[2] Phys. Rev. A 84, 063623 (2011).

[3] AVS Quantum Sci. 6, 10.1116/5.0175683 (2024).

[4] Rep. Prog. Phys. 81, 066201 (2018).

[5] Rev. Mod. Phys. 90, 035005 (2018).

[6] Phys. Rev. Lett. 127, 140402 (2021).   

Relativistic Center-of-mass and Relative Coordinates in Curved Spacetime – Relativistic Signatures in Atom Interferometry

Recently, quantum clock interferometry has been suggested for tests of the universality of free fall and the universality of gravitational redshift [1, 2]. The relativistic mass defect, i.e., the atomic mass depending on the internal state, plays a crucial role in these interferometer schemes. Sonnleitner and Barnett [3] calculated first-order relativistic corrections and included them into the multipolar atom-light Hamiltonian. They used (special) relativistic center-of-mass (COM) and relative coordinates first presented by Osborn and Close [4, 5] to decouple the COM and relative dynamics so that all remaining cross terms in the Hamiltonian can be interpreted as a state-dependent atomic mass. Schwartz [6] extended this work to curved spacetime and showed that these special-relativistic COM and relative coordinates do not remove all cross terms between the internal and external dynamics. Since these coordinates are determined by the generators of the Poincaré group for flat spacetime only, we show how to generalize them to curved spacetime. With explicit examples, we apply our results to calculate general-relativistic correction terms for atom interferometric sequences in a straight-forward manner.

References:

[1] Roura, Phys. Rev. X, 10:021014, Apr 2020.

[2] Ufrecht et al., Phys. Rev. Research, 2:043240, Nov 2020.

[3] Sonnleitner and Barnett, Phys. Rev. A, 98:042106, Oct 2018.

[4] Osborn, Phys. Rev., 176:1514–1522, Dec 1968.

[5] Close and Osborn, Phys. Rev. D, 2:2127–2140, Nov 1970.

[6] Schwartz, PhD thesis, Gottfried Willhelm Leibniz Universität Hannover, 2020.   

Fresnel Zone Plate Ring Waveguides for Improved Atom Interferometer Sensors

The sensitivity of an atomic interferometer is directly proportional to the area enclosed by the interferometer arms. This dependence is at odds with the aim of producing low Size, Weight, and Power (SWaP) sensor packages. Using atomic waveguides to maximise the enclosed area is a well-established technique for optimising these systems whilst reducing the overall size. We present a scheme for using Fresnel Zone Plates (FZPs) to produce smooth ring-shaped optical potentials to act as atomic waveguides and present a method for the loading of cold rubidium atoms into these rings. With the use of a shaped high-power 1064nm beam incident on our FZP, we produce the ring potential and, using an optical relay system, reimage it into our vacuum chamber. Both red and grey optical molasses are then utilised to cool the atoms to approximately 3.5μK (at a phase space density of 2.67×10^-4) for loading into our chosen ring-shaped waveguide of radius 0.5mm, waist size 10μm, and approximate depth 19.9μK. This work presents a key step towards the realisation of low SWaP, high sensitivity atom interferometer sensor packages.   

Laser Wavefront Engineering and Metrology using Point Source Atom Interferometry with 3-D Imaging Reconstruction

In atom interferometry, spatial wavefront aberrations from the atom optics laser beam can induce phase shifts in the atom cloud and result in major systematic phase shift errors and dephasing. The transverse Fourier components of such spatial laser aberration can be sampled in a point source atom interferometer by establishing position-velocity correlation through ballistic expansion. In this talk, we elaborate on the mapping correspondence of laser wavefront aberration and interference pattern on the atom cloud. For precise imaging of such interference, we present 3D image reconstruction using differential ray-tracing and modern neural rendering techniques. Various laser wavefront engineering techniques are also discussed as we showcase our machine learning enhanced wavefront metrology protocol.   

Explanation of a nonlinear phenomenon based on modified electromagnetic wave concept

The photon concept can explain almost all phenomena of light but it has few limitations. The energy equation of the photon is not suitable for high intensive light such as a laser. Also it cannot explain the intensity effect of the photoelectric effect. The energy of a photon at constant frequency remains unchanged even if the intensity of the light changes. If a photon collides with an electron and the electron absorbs the total energy of the photon. Then, the kinetic energy of the electron should remain constant at constant frequency even as the intensity of the light changes. This logical fact of the photon concept does not match with the experimental results of the photo-electron ejection. To solve the nonlinear problems, we have modified the electromagnetic (EM) wave theory. The frequency has been added to the Poynting vector. Also, we have shown that the phase difference between the electric and magnetic fields of the EM waves is 90 degrees. After that, the photoelectric effect has been explained by the modified EM wave concept. Accordingly, the electrons rotate under light. The half portion of the circular path of the surface electron is situated outside of the photocell. So, the electron comes out from the photocell at a moment of a time period. The frequency of the rotation is equal to the frequency of the light. And the value of the radius of the circular path is proportional to the values of the electric and magnetic field as well as the intensity of light. The concept reveals that the kinetic energy (as well as the value of the linear velocity, V = 2pfr) of the rotational electron depends on both the frequency and the intensity of light. The frequency and intensity effects of the photoelectric effect have been observed by an experiment. The experimental observations have been matched with the theoretical explanation smoothly. The orbital electron transition process and some more phenomena of the particle nature of light have been explained by the new process. The nonlinear (and also linear) phenomena such as harmonic and non harmonic generations, anti-Stokes scattering etc. are explainable by the modified EM wave concept easily. It is expected that the explanations will create an innovative dimension in the field of classical theory of light, which may increase in all areas of the quantum mechanics.   

Reveal the nature of Planck's constant

Elementary particles are two elemental charges orbiting each other, which is a model of the optical quantum, regardless of the law that exists in the following is M^2R=Q, where M is the mass of the inter-rotating elemental charge, R is the radius of the inter-orbiting elemental charge, and Q is a constant. The mass originates from the orbital velocity of the elemental charge, the mass of the elemental charge m = kv, v is the linear velocity of the elemental charge, m is the mass of the elemental charge, and k is the proportionality constant. Based on the energy of the photon E=hγ, Planck's constant can be considered as momentum × displacement. where the displacement should be the radius of the elemental charges orbiting each other, and Planck's constant can be written as h=MvR, which is the angular momentum of the elementary particle. Since m=kv, M^2R=Q, h=MvR=MMR/k=M^2R/K=Q/K, since Q and k are constants, h must be constants, the angular momentum of the elementary particles is conserved, and the value of the angular momentum of the elementary particles is Planck's constant   

The divergence of bosonic thermalization rates driven by the competition between finite temperature and quantum coherence

The thermalization of an isolated quantum system is described by quantum mechanics and thermodynamics, while these two subjects are still not fully consistent with each other. This leaves a less-explored region for what happens under both quantum and thermal effects, and the ultracold atom platform provides a suitable and versatile testbed to experimentally investigate these complex phenomena. Here we perform experiments based on ultracold atoms in optical lattices and observe a divergence of thermalization rates of quantum matters when the temperature approaches zero. By ramping an external parameter in the Hamiltonian, we observe the time delay between the internal relaxation and the external ramping. This provides us with a direct comparison of the thermalization rates of different quantum phases. We find that the quantum coherence and bosonic stimulation of superfluid induces the divergence while the non-zero thermal temperature and the many-body interactions are suppressing the divergence. The quantum coherence and the thermal effects are competing with each other in this isolated thermal quantum system. Besides these findings, our experiment shows that the divergence of critical exponents can also happen in a clean system without disorders and recent observations in superconductors cannot fully support the existence of Griffiths singularity.   

Multi-excitation scattering in atomic arrays

In free space, photons only weakly couple to single atoms. However, recent research has shown that arranging atoms in arrays with subwavelength lattice spacings can enable efficient and controlled interactions between free-space photons and atomic media. These systems exhibit collective atomic excitations with extraordinarily long lifetimes (i.e., subradiant states) and are promising for quantum information applications. To fully leverage their potential, it is crucial to understand how to manipulate multiple excitations (both photonic and atomic) in the presence of atomic nonlinearities. Although the theory of single excitation is well-established, studies of multiple excitations often rely on numerical methods, and a comprehensive theoretical framework for general interactions is still lacking. In this work, we develop a scattering formalism to investigate few-excitation interactions between photons and atomic excitations that applies to general atomic nonlinearities. Our method can be used to explore the generation of multi-excitation subradiance and non-classical light in subwavelength atomic arrays.