Ultra-Cold Atoms/Bose-Einstein Condensates
Ultra-Cold Atoms/Bose-Einstein Condensates
Ensembles of ultra-cold atoms can be used for various applications ranging from quantum memories and quantum sensors to quantum simulation. When clouds of bosonic atoms are cooled and compressed sufficiently, a large fraction of atoms occupy the state of lowest energy and a collective wave function arises. This phenomenon of Bose-Einstein condensation was first achieved in 1995, which led to the 2001 Nobel Prize in Physics being awarded to Cornell and Wieman [1] and Ketterle [2]. Since then, experimentalists have gained a significantly higher level of control over BECs through technological and methodological advancements; BECs can be created at temperatures down to the pico-kelvin scale [3], created and manipulated on an atom-chip [4], and have even been sent to space [5], allowing fundamental research in a microgravity environment.
In state-of-the-art technology, BECs are used for high precision measurements of forces [6] by means of matter-wave interferometry, where the wave function of each atom is split into two wave packets that are sent on different paths and then brought into interference. Atom-atom interactions that are always present are usually not an advantage in such applications but a nuisance. In contrast, atom-atom interactions are crucial in another possible use of BECs as force sensors; to measure the forces' effect on the collective oscillations of the atoms in the BEC. One specific example is the measurement of the thermal Casimir-Polder (CP) force [7].
Collaborators and I have investigated the sensing abilities of quasiparticle excitations of collective oscillations in BECs for gravity gradients [8] and oscillating gravitational fields [9]. In the latter case, we have shown that, in principle, it should be possible to detect small oscillating masses in the milligram-range. The possilities to employ quasipartices in BECs for sensing tasks are limited by noise and decoherence. In [10], Ralf Schützhold and I have investigated the strong detrimental effect of the omnipresent three-body loss in BECs, where three atoms collide, two form a molecule and the third one escapes with the excess energy.
An important question is how to prepare, manipulate and measure quasiparticle states of BECs. Quasiparticle excitations can be created with light pulses [11] and periodic modulations of the trap potential [12]. Measurement methods include self-interference of the Bose gas after release from the trap denoted as heterodyning [11] and in situ phase contrast imaging [13]. Placed in high finesse optical resonators, phonons in BECs can be strongly coupled to photons to obtain a quantum optomechanical system [14], where probe states can be prepared efficiently and measurements can be performed non-distructively. In [15], Benjamin Maaß, Daniel Hartely, Kurt Busch and I followed this cavity-optomechanical approach and discussed its use for gravimetry and other metrological applications.
Besides force sensing, another very prominent application of ultra-cold atomic gases is the simulation of other physical phenomena. One example is the quantum simulation of condensed matter systems [16]. Another example is the simulation of gravitational interactions. This can be done, for example, in quantum gases that interact via their dipoles [17,18]. It has been shown that similar interactions can be induced in BECs by strong light fields in a dedicated experiment [19] that I had the opportunity to provide some theoretical input for.
Quasiparticle excitations of BECs can also be employed for simulation tasks, for example, for the simulation of fundamental properties of quantum fields like the area law of mutual information [20] or the creation of excitations from the quantum vacuum by parametric driving, the dynamical Casimir effect [12]. Another interesting application of phonons in BECs that has become available in the last years is Analogue Gravity [21]. The approach is best denoted as analogue spacetime simulations: the effects of a curved or dynamically evolving spacetime on its matter content (neglecting any back reaction on the spacetime) is simulated in a system that can be created in the laboratory. BECs are a particular example of a class of systems that serve this purpose especially well: the matter content of spacetime is represented by the quasiparticle excitation; the analogue spacetime is emergent in the sense that, to some approximation in the appropriate regime, the dynamical evolution of quasiparticles is described by equations equivalent to those governing matter fields in cosmology and in gravitational background fields. Among a large variety of interesting theoretical proposals, as a specific example, Daniel Hartley, Tupac Bravo, Richard Howl, Ivette Fuentes and I, have proposed the simulation of gravitational waves acting on matter fields [22]. A particularly interesting experimental example is the simulation of curved light paths [23] and the simulation of Hawking radiation [24].
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[2] Stamper-Kurn, D. M., et al. "Collisionless and hydrodynamic excitations of a Bose-Einstein condensate." Physical Review Letters 81.3 (1998): 500. https://doi.org/10.1103/PhysRevLett.81.500
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[4] Schumm, Thorsten, et al. "Matter-wave interferometry in a double well on an atom chip." Nature physics 1.1 (2005): 57-62. https://doi.org/10.1038/nphys125
[5] Becker D., et al. "Space-borne Bose–Einstein condensation for precision interferometry." Nature 562.7727 (2018): 391-395. https://doi.org/10.1038
[6] Cronin A.D., Schmiedmayer J., and Pritchard D.E. "Optics and interferometry with atoms and molecules." Reviews of Modern Physics 81.3 (2009): 1051. https://doi.org/10.1103/RevModPhys.81.1051; pdf available here
[7] Obrecht, J.M., et al. "Measurement of the temperature dependence of the Casimir-Polder force." Physical review letters 98.6 (2007): 063201. https://doi.org/10.1103/PhysRevLett.98.063201
[8] Bravo T., Rätzel D., Fuentes I. "Phononic gravity gradiometry with Bose-Einstein condensates" Preprint: arxiv.org/abs/2001.10104
[9] Rätzel D., Howl R., Lindkvist J., Fuentes I., "Dynamical response of Bose-Einstein condensates to oscillating gravitational fields" New J. Phys. 20 073044 (2018), doi.org/10.1088/1367-2630/aad272; Preprint arxiv.org/abs/1804.11122
[10] Rätzel D., Schützhold R. “Decay of quantum sensitivity due to three-body loss in Bose-Einstein condensates” Phys. Rev. A 103, 063321 (2021), doi.org/10.1103/PhysRevA.103.063321; Preprint arxiv.org/abs/2101.05312
[11] Katz N., et al. "High sensitivity phonon spectroscopy of bose-einstein condensates using matter-wave interference." Physical review letters 93.22 (2004): 220403. https://doi.org/10.1103/PhysRevLett.93.220403
[12] Jaskula J-C., et al. "Acoustic analog to the dynamical Casimir effect in a Bose-Einstein condensate." Physical Review Letters 109.22 (2012): 220401. https://doi.org/10.1103/PhysRevLett.109.220401
[13] Stamper-Kurn D. M., et al. "Collisionless and hydrodynamic excitations of a Bose-Einstein condensate." Physical Review Letters 81.3 (1998): 500. https://doi.org/10.1103/PhysRevLett.81.500
[14] Ritsch H., et al. "Cold atoms in cavity-generated dynamical optical potentials." Reviews of Modern Physics 85.2 (2013): 553. https://doi.org/10.1103/RevModPhys.85.553; Preprint http://128.84.21.203/abs/1210.0013
[15] Maaß B., Hartley D., Busch K., Rätzel D. “Modulated light potentials for state manipulation of quasiparticles in ultra-cold Bose gases”, New Journal of Physics 24.4 (2022): 043014, https://doi.org/10.1088/1367-2630/ac5e17; Preprint: arxiv.org/abs/2111.10163
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[17] O'dell D. et al. "Bose-Einstein condensates with 1/r interatomic attraction: Electromagnetically induced “gravity”." Physical Review Letters 84.25 (2000): 5687. https://doi.org/10.1103/PhysRevLett.84.5687
[18] Artemiev A. I., et al. "Electromagnetically-induced isothermal" gravitational" collapse in molecular fermionic gases." International Journal of Modern Physics B 18.14 (2004): 2027-2034. https://doi.org/10.1142/S0217979204025099
[19] Maiwöger M., Sonnleitner M., Zhang T., Mazets I., Mallweger M., Rätzel D., Borselli F., Erne S., Schmiedmayer J., Haslinger P. “Observation of Light-Induced Dipole-Dipole Forces in Ultracold Atomic Gases” Physical Review X 12 (3), 031018, https://doi.org/10.1103/PhysRevX.12.031018; Preprint: arxiv.org/abs/2202.00562
[20] Mohammadamin T., et al. "Verification of the area law of mutual information in a quantum field simulator." Nature Physics (2023): 1-5. https://doi.org/10.1038/s41567-023-02027-1
[21] Barceló C., Liberati S., Visser M.. "Analogue gravity." Living reviews in relativity 14 (2011): 1-159. https://doi.org/10.12942/lrr-2011-3
[22] Hartley D., Bravo T., Rätzel D., Howl R., Fuentes I., “Analogue simulation of gravitational waves in a 3+1 dimensional Bose-Einstein condensate", Physical Review D 98 (2018), 025011, doi.org/10.1103/PhysRevD.98.025011; Preprint arxiv.org/abs/1712.01140
[23] Tajik, Mohammadamin, et al. "Experimental observation of curved light-cones in a quantum field simulator." Proceedings of the National Academy of Sciences 120.21 (2023): e2301287120. https://doi.org/10.1073/pnas.2301287120
[24] Muñoz de Nova, Juan Ramón, et al. "Observation of thermal Hawking radiation and its temperature in an analogue black hole." Nature 569.7758 (2019): 688-691. https://doi.org/10.1038/s41586-019-1241-0