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Scientific Reports

Observation of sub-wavelength phase structure of matter wave with two-dimensional optical lattice by Kapitza-Dirac diffraction

Kai Wen, Zengming Meng, Pengjun Wang, Liangwei Wang, Liangchao Chen, Lianghui Huang, Lihong Zhou, Xiaoling Cui, Jing Zhang

Published Apr 3, 2020• 8 citations
Publisher

Abstract

We report an experimental demonstration of generation and measurement of sub-wavelength phase structure of a Bose-Einstein condensate (BEC) with two-dimensional optical lattice. This is implemented by applying a short lattice pulse on BEC in the Kapitza-Dirac (or Raman-Nath) regime, which, in the classical picture, corresponds to phase modulation imprinted on matter wave. When the phase modulation is larger than 2π in a lattice cell, the periodicity of phase naturally forms the sub-wavelength phase structure. By converting the phase information into amplitude, we are able to measure the sub-wavelength structure through the momentum distribution of BEC via the time-of-flight absorption image. Beyond the classical treatment, we further demonstrate the importance of quantum fluctuations in the formation of sub-wavelength phase structure by considering different lattice configurations. Our scheme provides a powerful tool for exploring the fine structure of a lattice cell as well as topological defects in matter wave.

DOI
10.1038/s41598-020-62551-5

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We report an experimental demonstration of generation and measurement of sub-wavelength phase structure of a Bose-Einstein condensate (BEC) with two-dimensional optical lattice. This is implemented by applying a short lattice pulse on BEC in the Kapitza-Dirac (or Raman-Nath) regime, which, in the classical picture, corresponds to phase modulation imprinted on matter wave. When the phase modulation is larger than 2π in a lattice cell, the periodicity of phase naturally forms the sub-wavelength phase structure. By converting the phase information into amplitude, we are able to measure the sub-wavelength structure through the momentum distribution of BEC via the time-of-flight absorption image. Beyond the classical treatment, we further demonstrate the importance of quantum fluctuations in the formation of sub-wavelength phase structure by considering different lattice configurations. Our scheme provides a powerful tool for exploring the fine structure of a lattice cell as well as topological defects in matter wave.
We report an experimental demonstration of engineering phase wraps for sub-wavelength structure in a Bose-Einstein condensate (BEC) with two-dimensional optical lattices. A short lattice pulse is applied on BEC working in the Kapitza-Dirac (or Raman-Nath) regime, which corresponds to phase modulation imprint on matter wave. When the phase modulation on matter wave is larger than 2π2π2π in a lattice cell, there appears phase wraps with multiple 2π2π2π jumps, generating the sub-wavelength phase structure. The phase wraps for sub-wavelength structure are measured in momentum space via the time-of-flight absorption image, which corresponds to converting phase information into amplitude. %Two different kinds of two-dimensional optical lattice are studied, which show the different subwavelength phase structure. Moreover, we identify an additional condition for the validity of Kapitza-Dirac regime, which relies crucially on the lattice configurations. This scheme can be used for studying the property of optical lattices and topological defects in matter wave.
We study 87Rb Bose-Einstein condensation (BEC) loading into the pulse of the one-dimensional (1D) optical lattice experimentally. The lattice is turned on abruptly, held constant for a variable time, and then turned off abruptly. The measurement of the depth of the optical lattice is obtained by Kapitza-Dirac scattering. The temporal matter-wave-dispersion Talbot effect with 87Rb BEC is observed by applying a pair of pulsed standing waves (as pulsed phase gratings) with the separation of a variable delay.
Quantum gases in optical lattices allow for fundamental studies in atomic and condensed-matter physics and the exploration of novel effects. After a brief introduction to the fundamentals of quantum gas experiments in optical lattices, we discuss two recent experiments focusing on driven matter waves in a one-dimensional optical lattice. The first experiment uses a tilted bichromatic optical lattice to investigate the interplay of disorder and collisional interactions in the accelerated transport of a Bose-Einstein condensate. Here, a screening effect is observed, in which the interactions effectively cancel the damping of Bloch oscillations induced by a (quasi-)disordered potential. This effect can be understood through a modification of the underlying band structure by the interactions. The second experiment studies the dynamics of a weakly trapped condensate resonantly coupled to the orbitals of a strongly confining state-selective lattice. We observe momentum distributions that correspond to matter wave diffraction from a periodic structure; however, the diffractive dynamics remain strongly linked to the internal-state Rabi oscillations. In the regime investigated, which we call the nonadiabatic regime, no diffracting potential can be defined. We show how only for much stronger coupling, the internal and external dynamics decouple, transitioning from nonadiabatic diffraction to the well-studied Kapitza-Dirac diffraction. We further investigate prospects for realizing dissipative spin models in our ultracold atomic gas experiment. To this end, we develop and test in the laboratory several possible implementations of effective spins with differential coupling to a superfluid background and examine their viability for a realization of the spin-boson model. | 94 pages
Dual lattices such as honeycomb and hexagonal lattices typically obey Babinet's principle in optics, which states that the expected interference patterns of two complementary diffracting objects are identical and indistinguishable, except for their overall intensity. Here, we study Kapitza--Dirac diffraction of Bose--Einstein condensates in optical lattices and find that matter waves in dual lattices obey Babinet's principle only under the condition of weak-pulse Raman--Nath regimes. In contrast, the Kapitza--Dirac matter-wave diffraction in the strong-pulse Raman--Nath regime (corresponding to the phase wrapping method we developed to generate sub-wavelength phase structures in Sci. Rep. 10, 5870 (2020)) can break Babinet's principle and clearly resolve the distinct interference patterns of the dual honeycomb and hexagonal lattices. This method offers exceptional precision in characterizing lattice configurations and advance the study of symmetry-related phenomena, overcoming the limitations of real-space imaging.
We study the phase coherence property of Bose−Einstein condensates confined in a one-dimensional optical lattice formed by a standing-wave laser field. The lattice depth is determined using a method of Kapitza–Dirac scattering between a condensate and a short pulse lattice potential. Condensates are then adiabatically loaded into the optical lattice. The phase coherence property of the confined condensates is reflected by the interference patterns of the expanded atomic cloud released from the optical lattice. For weak lattice, nearly all of the atoms stay in a superfluid state. However, as the lattice depth is increased, the phase coherence of the whole condensate sample is gradually lost, which confirms that the sub-condensates in each lattice well have evolved into number-squeezed states.
In this thesis, I study the properties of cold neutral atoms, including Bose-Einstein condensates (BEC), inside periodic light-shift potentials created by optical lattices. In the first part, a new optical-lattice scheme, employing Raman transitions, hereafter referred to as a Raman Optical Lattice (ROL), is investigated. This optical lattice possesses a novel sub-Doppler cooling mechanism and a reduced periodicity. Both theoretical and experimental results con¯rm these two characteristics of the ROL. In the second half of the thesis, instead of thermal atoms, optical lattices are loaded with condensate atoms. Our BEC apparatus and the procedure towards forming a BEC are described in detail. After the achievement of the BEC, a 1D far-detuned optical lattice is applied to the BEC. A number of phenomena are observed, including Kapitza-Dirac diffraction, thermal atom interference, atom interferometry, Bloch oscillations, and a superfluid to Mott-insulator transition. Finally a brief discussion about future work is given.