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Journal articles on the topic 'Sideband cooling'

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Author: Grafiati
Published: 14 March 2023

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1

Mielke, J., J. Pick, J. A. Coenders, T. Meiners, M. Niemann, J. M. Cornejo, S. Ulmer, and C. Ospelkaus. "139 GHz UV phase-locked Raman laser system for thermometry and sideband cooling of 9Be+ ions in a Penning trap." Journal of Physics B: Atomic, Molecular and Optical Physics 54, no. 19 (October 6, 2021): 195402. http://dx.doi.org/10.1088/1361-6455/ac319d.

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Abstract We demonstrate the phase locking of two ultraviolet (UV) laser sources by modulating a fundamental infrared (IR) laser with fourth-order sidebands using an electro-optic modulator and the phase locking of one sideband to a second fundamental IR laser. Subsequent sum frequency generation and second harmonic generation successfully translates the frequency offset to the UV domain. The phase lock at 139 GHz is confirmed through stimulated Raman transitions for the thermometry of 9Be+ ions confined in a cryogenic Penning trap. This technique might be used for the sideband cooling of single 9Be+ ions as well as sympathetic cooling schemes and quantum-logic-based measurements in Penning traps in the future.
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2

Wells, Ann Laurie, and Richard J. Cook. "Simple theory of sideband cooling." Physical Review A 41, no. 7 (April 1, 1990): 3916–23. http://dx.doi.org/10.1103/physreva.41.3916.

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3

Bao, Yang, Qinghong Liao, Qingmin Zhao, and Jing Wu. "Suppression of Stokes heating processes and improved optomechanical cooling with frequency modulation." Communications in Theoretical Physics 74, no. 4 (April 1, 2022): 045102. http://dx.doi.org/10.1088/1572-9494/ac5588.

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Abstract Ground-state cooling of mesoscopic mechanical objects is still a major challenge in the unresolved-sideband regime. We present a frequency modulation (FM) scheme to achieve cooling of the mechanical resonator to its ground-state in a double-cavity optomechanical system containing a mechanical resonator. The mean phonon number is determined by numerically solving a set of differential equations derived from the quantum master equations. Due to efficient suppression of Stokes heating processes in the presence of FM, the ground-state cooling, indicated by numerical calculations, is significantly achievable, regardless of whether in the resolved-sideband regime or the unresolved-sideband regime. Furthermore, by choosing parameters reasonably, the improvement of the quantum cooling limit is found to be capable of being positively correlated with the modulation frequency. This method provides new insight into quantum manipulation and creates more possibilities for applications of quantum devices.
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4

Zhao, Daiyue, Shaopeng Liu, Junfeng Wang, Yaya Mao, Ying Li, and Bo Liu. "Simultaneous measurement for amplitude and frequency of time-harmonic force based on optomechanically induced nonlinearity." Journal of Applied Physics 131, no. 10 (March 14, 2022): 104401. http://dx.doi.org/10.1063/5.0085477.

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An accurate readout of the mechanical motion using optomechanical coupling is highly desired for on-chip sensing applications but it remains challenging due to the uncertainty caused by time-dependent parameters and noisy fluctuations. Here, we propose an efficient scheme to realize simultaneous measurement for both amplitude and frequency of the time-harmonic force (THF) in a hybrid optomechanical system via a nonlinear sum sideband effect. In this optomechanical system assisted by a degenerate parametric amplifier (DPA), the nonlinear optomechanical interaction between the external THF, optical, and mechanical modes is used to construct the frequency component of optical sum sidebands. Using experimentally achievable parameters, we find that the conversion efficiency of the sum sidebands has a significant enhancement when the nonlinear gain coefficient of DPA increases. In the scheme of the dual-parameter measurement, we also report that the amplitude of THF could be independently detected by observing the intensity variation of the lower sum sideband, while the frequency of THF could be separately read by monitoring the frequency of the prominent peak in this nonlinear spectrum. Benefitting from the optical cooling of a mechanical element, the theoretical results show that the minimum resolutions for detecting the amplitude and the frequency of THF are approximately [Formula: see text] and [Formula: see text], respectively.
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5

Schliesser, A., R. Rivière, G. Anetsberger, O. Arcizet, and T. J. Kippenberg. "Resolved-sideband cooling of a micromechanical oscillator." Nature Physics 4, no. 5 (April 13, 2008): 415–19. http://dx.doi.org/10.1038/nphys939.

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6

Guo, Jingkun, and Simon Gröblacher. "Coherent feedback in optomechanical systems in the sideband-unresolved regime." Quantum 6 (November 3, 2022): 848. http://dx.doi.org/10.22331/q-2022-11-03-848.

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Preparing macroscopic mechanical resonators close to their motional quantum groundstate and generating entanglement with light offers great opportunities in studying fundamental physics and in developing a new generation of quantum applications. Here we propose an experimentally interesting scheme, which is particularly well suited for systems in the sideband-unresolved regime, based on coherent feedback with linear, passive optical components to achieve groundstate cooling and photon-phonon entanglement generation with optomechanical devices. We find that, by introducing an additional passive element – either a narrow linewidth cavity or a mirror with a delay line – an optomechanical system in the deeply sideband-unresolved regime will exhibit dynamics similar to one that is sideband-resolved. With this new approach, the experimental realization of groundstate cooling and optomechanical entanglement is well within reach of current integrated state-of-the-art high-Q mechanical resonators.
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7

Peik, E., J. Abel, Th Becker, J. von Zanthier, and H. Walther. "Sideband cooling of ions in radio-frequency traps." Physical Review A 60, no. 1 (July 1, 1999): 439–49. http://dx.doi.org/10.1103/physreva.60.439.

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8

Morigi, G., J. Eschner, J. I. Cirac, and P. Zoller. "Laser cooling of two trapped ions: Sideband cooling beyond the Lamb-Dicke limit." Physical Review A 59, no. 5 (May 1, 1999): 3797–808. http://dx.doi.org/10.1103/physreva.59.3797.

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9

Wei, Chun-Hua, and Shu-Hua Yan. "Raman sideband cooling of rubidium atoms in optical lattice." Chinese Physics B 26, no. 8 (August 2017): 080701. http://dx.doi.org/10.1088/1674-1056/26/8/080701.

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10

Park, Young-Shin, and Hailin Wang. "Resolved-sideband and cryogenic cooling of an optomechanical resonator." Nature Physics 5, no. 7 (June 7, 2009): 489–93. http://dx.doi.org/10.1038/nphys1303.

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11

Li, Guo-Hui, and Xin-Ye Xu. "Raman Sideband Cooling of Two-Valence-Electron Fermionic Atoms." Chinese Physics Letters 28, no. 6 (June 2011): 063203. http://dx.doi.org/10.1088/0256-307x/28/6/063203.

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12

Sawamura, H., K. Kanda, R. Yamazaki, K. Toyoda, and S. Urabe. "Optimum parameters for sideband cooling of a 40Ca+ ion." Applied Physics B 93, no. 2-3 (September 8, 2008): 381–88. http://dx.doi.org/10.1007/s00340-008-3162-8.

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13

Marzoli, I., J. I. Cirac, R. Blatt, and P. Zoller. "Laser cooling of trapped three-level ions: Designing two-level systems for sideband cooling." Physical Review A 49, no. 4 (April 1, 1994): 2771–79. http://dx.doi.org/10.1103/physreva.49.2771.

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14

Zhang, Shuo, Jian-Qi Zhang, Wei Wu, Wan-Su Bao, and Chu Guo. "Fast cooling of trapped ion in strong sideband coupling regime." New Journal of Physics 23, no. 2 (February 1, 2021): 023018. http://dx.doi.org/10.1088/1367-2630/abe273.

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15

Karuza, M., C. Molinelli, M. Galassi, C. Biancofiore, R. Natali, P. Tombesi, G. Di Giuseppe, and D. Vitali. "Optomechanical sideband cooling of a thin membrane within a cavity." New Journal of Physics 14, no. 9 (September 17, 2012): 095015. http://dx.doi.org/10.1088/1367-2630/14/9/095015.

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16

Clark, Jeremy B., Florent Lecocq, Raymond W. Simmonds, José Aumentado, and John D. Teufel. "Sideband cooling beyond the quantum backaction limit with squeezed light." Nature 541, no. 7636 (January 2017): 191–95. http://dx.doi.org/10.1038/nature20604.

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17

Blockley, C. A., and D. F. Walls. "Cooling of a trapped ion in the strong-sideband regime." Physical Review A 47, no. 3 (March 1, 1993): 2115–27. http://dx.doi.org/10.1103/physreva.47.2115.

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18

de Matos Filho, R. L., and W. Vogel. "Second-sideband laser cooling and nonclassical motion of trapped ions." Physical Review A 50, no. 3 (September 1, 1994): R1988—R1991. http://dx.doi.org/10.1103/physreva.50.r1988.

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19

Teufel, J. D., T. Donner, Dale Li, J. W. Harlow, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, K. W. Lehnert, and R. W. Simmonds. "Sideband cooling of micromechanical motion to the quantum ground state." Nature 475, no. 7356 (July 2011): 359–63. http://dx.doi.org/10.1038/nature10261.

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20

Han, Dian-Jiun, Steffen Wolf, Steven Oliver, Colin McCormick, Marshall T. DePue, and David S. Weiss. "3D Raman Sideband Cooling of Cesium Atoms at High Density." Physical Review Letters 85, no. 4 (July 24, 2000): 724–27. http://dx.doi.org/10.1103/physrevlett.85.724.

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21

Morigi, G., H. Baldauf, W. Lange, and H. Walther. "Raman sideband cooling in the presence of multiple decay channels." Optics Communications 187, no. 1-3 (January 2001): 171–77. http://dx.doi.org/10.1016/s0030-4018(00)01109-3.

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22

Evers, J., and C. H. Keitel. "Double-EIT ground-state laser cooling without blue-sideband heating." Europhysics Letters (EPL) 68, no. 3 (November 2004): 370–76. http://dx.doi.org/10.1209/epl/i2004-10207-5.

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23

Yang, Cheng, Lin Zhang, and Weiping Zhang. "Squeezed cooling of mechanical motion beyond the resolved-sideband limit." EPL (Europhysics Letters) 122, no. 1 (April 1, 2018): 14001. http://dx.doi.org/10.1209/0295-5075/122/14001.

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24

Hilico, Laurent, Jean-Philippe Karr, Albane Douillet, Paul Indelicato, Sebastian Wolf, and Ferdinand Schmidt Kaler. "Preparing single ultra-cold antihydrogen atoms for free-fall in GBAR." International Journal of Modern Physics: Conference Series 30 (January 2014): 1460269. http://dx.doi.org/10.1142/s2010194514602695.

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We discuss an experimental approach allowing to prepare antihydrogen atoms for the GBAR experiment. We study the feasibility of all necessary experimental steps: The capture of incoming [Formula: see text] ions at keV energies in a deep linear RF trap, sympathetic cooling by laser cooled Be + ions, transfer to a miniaturized trap and Raman sideband cooling of an ion pair to the motional ground state, and further reducing the momentum of the wavepacket by adiabatic opening of the trap. For each step, we point out the experimental challenges and discuss the efficiency and characteristic times, showing that capture and cooling are possible within a few seconds.
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25

Stutter, G., P. Hrmo, V. Jarlaud, M. K. Joshi, J. F. Goodwin, and R. C. Thompson. "Sideband cooling of small ion Coulomb crystals in a Penning trap." Journal of Modern Optics 65, no. 5-6 (October 24, 2017): 549–59. http://dx.doi.org/10.1080/09500340.2017.1376719.

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26

Zhang, Jun, Qing Zhang, Xingzhi Wang, Leong Chuan Kwek, and Qihua Xiong. "Resolved-sideband Raman cooling of an optical phonon in semiconductor materials." Nature Photonics 10, no. 9 (July 4, 2016): 600–605. http://dx.doi.org/10.1038/nphoton.2016.122.

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27

Perrin, H., A. Kuhn, I. Bouchoule, and C. Salomon. "Sideband cooling of neutral atoms in a far-detuned optical lattice." Europhysics Letters (EPL) 42, no. 4 (May 15, 1998): 395–400. http://dx.doi.org/10.1209/epl/i1998-00261-y.

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28

Li, Ji-Xin, C. H. Raymond Ooi, Qiong Wang, and Sheng-Li Chang. "Simultaneous cooling coupled nano-mechanical resonators in cavity optomechanics." Laser Physics 33, no. 3 (February 7, 2023): 035202. http://dx.doi.org/10.1088/1555-6611/acb5a7.

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Abstract Coupled mechanical resonators have recently attracted great attention for both practical applications and fundamental studies. As a preparation step, it is needed to cool the coupled mechanical resonators to their ground states. Here we propose a theoretical scheme to cool two coupled mechanical resonators by introducing an optomechanical interface. The final mean phonon numbers of the two mechanical resonators are calculated exactly and the results show that the ground-state cooling is achievable in the resolved-sideband regime and under the optimal driving. Moreover, we derived analytical expressions of the cooling limits by adiabatically eliminating the cavity field under the large-decay limit.
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29

Sriarunothai, Theeraphot, Gouri Shankar Giri, Sabine Wölk, and Christof Wunderlich. "Radio frequency sideband cooling and sympathetic cooling of trapped ions in a static magnetic field gradient." Journal of Modern Optics 65, no. 5-6 (November 22, 2017): 560–67. http://dx.doi.org/10.1080/09500340.2017.1401137.

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30

Hamann, S. E., D. L. Haycock, G. Klose, P. H. Pax, I. H. Deutsch, and P. S. Jessen. "Resolved-Sideband Raman Cooling to the Ground State of an Optical Lattice." Physical Review Letters 80, no. 19 (May 11, 1998): 4149–52. http://dx.doi.org/10.1103/physrevlett.80.4149.

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31

Schulz, Stephan A., Ulrich Poschinger, Frank Ziesel, and Ferdinand Schmidt-Kaler. "Sideband cooling and coherent dynamics in a microchip multi-segmented ion trap." New Journal of Physics 10, no. 4 (April 30, 2008): 045007. http://dx.doi.org/10.1088/1367-2630/10/4/045007.

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32

Zhang, Jun, Qing Zhang, Xingzhi Wang, Leong Chuan Kwek, and Qihua Xiong. "Publisher Correction: Resolved-sideband Raman cooling of an optical phonon in semiconductor materials." Nature Photonics 13, no. 6 (April 25, 2019): 436. http://dx.doi.org/10.1038/s41566-019-0440-4.

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33

Vuletić, Vladan, Cheng Chin, Andrew J. Kerman, and Steven Chu. "Degenerate Raman Sideband Cooling of Trapped Cesium Atoms at Very High Atomic Densities." Physical Review Letters 81, no. 26 (December 28, 1998): 5768–71. http://dx.doi.org/10.1103/physrevlett.81.5768.

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34

Sarma, Bijita, and Amarendra K. Sarma. "Atom assisted cavity cooling of a micromechanical oscillator in the unresolved sideband regime." Journal of Physics: Conference Series 759 (October 2016): 012059. http://dx.doi.org/10.1088/1742-6596/759/1/012059.

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35

Yum, Dahyun, Tarun Dutta, Jasper Phua Sing Cheng, and Manas Mukherjee. "Optical Sideband Cooling of a Radial Motional Mode of a Trapped 138Ba+ Ion." Journal of the Korean Physical Society 77, no. 12 (November 19, 2020): 1143–47. http://dx.doi.org/10.3938/jkps.77.1143.

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36

Cui, Kai-feng, Jun-juan Shang, Si-jia Chao, Shao-mao Wang, Jin-bo Yuan, Ping Zhang, Jian Cao, Hua-lin Shu, and Xue-ren Huang. "Sympathetic sideband cooling of a 40Ca+–27Al+ pair toward a quantum logic clock." Journal of Physics B: Atomic, Molecular and Optical Physics 51, no. 4 (January 24, 2018): 045502. http://dx.doi.org/10.1088/1361-6455/aaa591.

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37

Huang, Sumei, and Aixi Chen. "Cooling of a Mechanical Oscillator and Normal Mode Splitting in Optomechanical Systems with Coherent Feedback." Applied Sciences 9, no. 16 (August 19, 2019): 3402. http://dx.doi.org/10.3390/app9163402.

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The ground state cooling of a mechanical oscillator and strong optomechanical coupling are necessary prerequisites for realizing quantum control of the macroscopic mechanical oscillator. Here, we show that the resolved-sideband cooling of a mechanical oscillator in an optomechanical system can be enhanced by a simple coherent feedback scheme, in which a portion of the output field from the cavity is fed back into the cavity using an asymmetric beam splitter. Moreover, we show that the normal mode splitting in the spectra of the movable mirror and the output field in a weakly coupled optomechanical system can be induced by the feedback scheme due to a reduced effective cavity decay rate. We find that the peak separation becomes larger and two peaks of the spectra become narrower and higher with increasing the reflection coefficient r of the beam splitter.
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38

Li, Y., J. Wu, G. Feng, J. Nute, S. Piano, L. Hackermüller, J. Ma, L. Xiao, and S. Jia. "Enhanced Raman sideband cooling of caesium atoms in a vapour-loaded magneto-optical trap." Laser Physics Letters 12, no. 5 (March 31, 2015): 055501. http://dx.doi.org/10.1088/1612-2011/12/5/055501.

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39

Monroe, C., D. M. Meekhof, B. E. King, S. R. Jefferts, W. M. Itano, D. J. Wineland, and P. Gould. "Resolved-Sideband Raman Cooling of a Bound Atom to the 3D Zero-Point Energy." Physical Review Letters 75, no. 22 (November 27, 1995): 4011–14. http://dx.doi.org/10.1103/physrevlett.75.4011.

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40

Kerman, Andrew J., Vladan Vuletić, Cheng Chin, and Steven Chu. "Beyond Optical Molasses: 3D Raman Sideband Cooling of Atomic Cesium to High Phase-Space Density." Physical Review Letters 84, no. 3 (January 17, 2000): 439–42. http://dx.doi.org/10.1103/physrevlett.84.439.

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41

Goham, Connor J. B., and Joseph W. Britton. "Resolved-sideband micromotion sensing in Yb+ on the 935 nm repump transition." AIP Advances 12, no. 11 (November 1, 2022): 115315. http://dx.doi.org/10.1063/5.0128113.

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Ions displaced from the potential minimum in an RF Paul trap exhibit excess micromotion. A host of well-established techniques are routinely used to sense (and null) this excessive motion in applications ranging from quantum computing to atomic clocks. The rich atomic structure of Yb+, a heavy ion, includes low-lying 2D3/2 states that must be repumped to permit Doppler cooling, typically using a 935 nm laser coupled to the 3D[3/2]1/2 states. In this article, we demonstrate the use of this transition to make resolved-sideband measurements of 3D micromotion in 172Yb+ and 171Yb+ ions. Relative to other sensing techniques, our approach has very low technical overhead and is distinctively compatible with surface-electrode ion traps.
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42

Schliesser, A., O. Arcizet, R. Rivière, G. Anetsberger, and T. J. Kippenberg. "Resolved-sideband cooling and position measurement of a micromechanical oscillator close to the Heisenberg uncertainty limit." Nature Physics 5, no. 7 (June 7, 2009): 509–14. http://dx.doi.org/10.1038/nphys1304.

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43

Cai, M. L., Z. D. Liu, Y. Jiang, Y. K. Wu, Q. X. Mei, W. D. Zhao, L. He, X. Zhang, Z. C. Zhou, and L. M. Duan. "Probing a Dissipative Phase Transition with a Trapped Ion through Reservoir Engineering." Chinese Physics Letters 39, no. 2 (February 1, 2022): 020502. http://dx.doi.org/10.1088/0256-307x/39/2/020502.

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Dissipation is often considered as a detrimental effect in quantum systems for unitary quantum operations. However, it has been shown that suitable dissipation can be useful resources in both quantum information and quantum simulation. Here, we propose and experimentally simulate a dissipative phase transition (DPT) model using a single trapped ion with an engineered reservoir. We show that the ion’s spatial oscillation mode reaches a steady state after the alternating application of unitary evolution under a quantum Rabi model Hamiltonian and sideband cooling of the oscillator. The average phonon number of the oscillation mode is used as the order parameter to provide evidence for the DPT. Our work highlights the suitability of trapped ions for simulating open quantum systems and shall facilitate further investigations of DPT with various dissipation terms.
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44

Abbassi, Mohammad Ali, and Khashayar Mehrany. "Employing coupled cavities to increase the cooling rate of a levitated nanosphere in the resolved sideband regime." Journal of the Optical Society of America B 35, no. 7 (June 11, 2018): 1563. http://dx.doi.org/10.1364/josab.35.001563.

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45

Jacobi, C., and D. Kürschner. "Long-term Measurements of Nighttime LF Radio Wave Reflection Heights over Central Europe." Advances in Radio Science 3 (May 13, 2005): 427–30. http://dx.doi.org/10.5194/ars-3-427-2005.

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Abstract. The nighttime ionospheric absolute reflection height of low-frequency (LF) radio waves at oblique incidence has been measured continuously since late 1982 using 1.8kHz sideband phase comparisons between the sky wave and the ground wave of a commercial 177kHz LF transmitter. The dataset allows the analysis of long-term trends and other regular variations of the reflection height. Beside the clear signal of the 11-year solar cycle a quasi-biennial oscillation is visible in LF reflection heights, which is correlated to the equatorial stratospheric wind field. A long-term decreasing reflection height trend is found, confirming results from other measurements and theoretical estimations. The results can be interpreted as a long-term decrease of the height levels of fixed electron density in the lower E region, reflecting a long-term cooling trend of the middle atmosphere.
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46

Li, Xiao, Theodore A. Corcovilos, Yang Wang, and David S. Weiss. "3D Projection Sideband Cooling." Physical Review Letters 108, no. 10 (March 9, 2012). http://dx.doi.org/10.1103/physrevlett.108.103001.

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47

Machado, João, and Yaroslav Blanter. "Optomechanical damping as the origin of sideband asymmetry." SciPost Physics Core 5, no. 2 (June 23, 2022). http://dx.doi.org/10.21468/scipostphyscore.5.2.034.

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Sideband asymmetry in cavity optomechanics has been explained by particle creation and annihilation processes, which bestow an amplitude proportional to 'n+1' and 'n' excitations to each of the respective sidebands. We discuss the issues with this as well as other interpretations, such as quantum backaction and noise interference, and show that the asymmetry is due to the optomechanical damping caused by the probe and the cooling lasers instead.
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48

Wang, Jin-Qi, Ang-Zhang, Cong-Cong Tian, Ni Yin, Qiang Zhu, Bing Wang, Zhuan-Xian Xiong, Ling-Xiang He, and Bao-Long Lv. "Effective sideband cooling in an ytterbium optical lattice clock." Chinese Physics B, February 10, 2022. http://dx.doi.org/10.1088/1674-1056/ac5392.

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Abstract Sideband cooling is a key technique for improving the performance of optical atomic clocks by preparing cold atoms and single ions into the ground vibrational state. In this work, we demonstrate detailed experimental research on pulsed Raman sideband cooling in a 171Yb optical lattice clock. A sequence comprised of interleave 578 nm cooling pulses resonant on the 1st-order red sideband and 1388 nm repumping pulses is carried out to transfer atoms into the motional ground state. We successfully decrease the axial temperature of atoms in the lattice from 6.5 µK to less than 0.8 µK in the trap depth of 24 µK, corresponding to an average axial motional quantum number <n z > < 0.03. Rabi oscillation spectroscopy is measured to evaluate the effect of sideband cooling on inhomogeneous excitation. The maximum excitation fraction is increased from 0.8 to 0.86, indicating an enhancement in the quantum coherence of the ensemble. Our work will contribute to improving the instability and uncertainty of Yb lattice clocks.
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49

Wang, Chun-Che, Yi-Cheng Wang, Chung-Hsien Wang, Chi-Chih Chen, and Hsiang-Hua Jen. "Superior dark-state cooling via nonreciprocal couplings in trapped atoms." New Journal of Physics, October 31, 2022. http://dx.doi.org/10.1088/1367-2630/ac9ed5.

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Abstract Cooling the trapped atoms toward their motional ground states is key to applications of quantum simulation and quantum computation. By utilizing nonreciprocal couplings between two atoms, we present an intriguing dark-state cooling scheme in $\Lambda$-type three-level structure, which is shown superior than the conventional electromagnetically-induced-transparency cooling in a single atom. The effective nonreciprocal couplings can be facilitated either by an atom-waveguide interface or a free-space photonic quantum link. By tailoring system parameters allowed in dark-state cooling, we identify the parameter regions of better cooling performance with an enhanced cooling rate. We further demonstrate a mapping to the dark-state sideband cooling under asymmetric laser driving fields, which shows a distinct heat transfer and promises an outperforming dark-state sideband cooling assisted by collective spin-exchange interactions.
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50

Schwedes, Ch, Th Becker, J. von Zanthier, H. Walther, and E. Peik. "Laser sideband cooling with positive detuning." Physical Review A 69, no. 5 (May 25, 2004). http://dx.doi.org/10.1103/physreva.69.053412.

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