Many-particle tunnelling in a driven Bosonic Josephson junction

Jinasundera, Tharanga; Weiß, Christoph; Holthaus, Martin

doi:10.1016/j.chemphys.2005.06.025

Cited by 37 publications

(36 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As follows from elementary estimates [3,4,11], the unperturbed two-mode Hamiltonian (1) can be trusted as long as the particle number N does not exceed the ratio of the characteristic length scale L of one of the wells and the scattering length a; for µm-sized traps filled with alkali atoms, this ratio L/a will typically be on the order of 1000. However, the ability to reduce atomic scattering lengths by means of Feshbach resonances [12] allows one to extend the two-mode approximation to much larger samples.…”

mentioning

confidence: 99%

“…Such a modulation of an optical double well can be achieved by periodically shifting the focus of a blue-detuned laser, which creates the barrier between the two wells, with the help of a piezoactuated mirror [1]. Thus, we are led to the explicitly time-dependent many-body HamiltonianAs follows from elementary estimates [3,4,11], the unperturbed two-mode Hamiltonian (1) can be trusted as long as the particle number N does not exceed the ratio of the characteristic length scale L of one of the wells and the scattering length a; for µm-sized traps filled with alkali atoms, this ratio L/a will typically be on the order of 1000. However, the ability to reduce atomic scattering lengths by means of Feshbach resonances [12] allows one to extend the two-mode approximation to much larger samples.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Analog of Photon-Assisted Tunneling in a Bose-Einstein Condensate

et al. 2005

Self Cite

View full text Add to dashboard Cite

We study many-body tunneling of a small Bose-Einstein condensate in a periodically modulated, tilted double-well potential. Periodic modulation of the trapping potential leads to an analog of photon-assisted tunneling, with distinct signatures of the interparticle interaction visible in the amount of particles transferred from one well to the other. In particular, under experimentally accessible conditions there exist well-developed half-integer Shapiro-like resonances.PACS numbers: 03.75. Lm, 74.50.+r In a recent experiment, it has become possible to monitor the Josephson-like oscillation of a sample of about 1000 Bose-Einstein-condensed atoms in an optical double-well potential, and to observe in situ both the evolution of the atomic densities, and of the relative phase between the condensates in both wells [1]. In the present Letter, we propose to extend such experiments by modulating the trapping potential periodically in time. As we will demonstrate, such modulated double-well condensates exhibit certain parallels to photon-assisted tunneling in microwave-driven superconducting Josephson junctions [2], although the "photons" now tend to fall into the lower Kilohertz regime.We consider a symmetric double-well trap filled with N Bose particles at temperature T = 0, as realized approximately in the Heidelberg experiment [1]. Denoting the tunneling splitting between the lowest pair of single-particle energy eigenstates by Ω, and adopting the common two-mode approximation [3,4,5], the system's Hamiltonian takes the idealized formwhere a ( †) i is the annihilation (creation) operator for a Boson in the i-th well, satisfying the commutation relation [a i , a † j ] = δ i,j (i, j = 1, 2). The on-site interaction energy of a single pair of Bosons occupying the same well is 2 κ, proportional to the s-wave scattering length of the particle species. This deceptively simple model (1), describing an unforced Bosonic Josephson junction, has recently been studied in considerable detail [6,7]. The key parameter governing its dynamics is the dimensionless ratio N κ/Ω. While the well-understood mean-field approximation [8, 9, 10] corresponds to the limit N → ∞ and κ → 0, taken such that the product N κ remains constant, present experiments start to explore the dynamics beyond the mean-field regime [1].We extend this system by introducing a twofold bias: We assume that the two wells are tilted such that their bottoms are misaligned in energy by an amount 2 µ 0 , which should be sufficiently large compared to the tunnel splitting Ω, so that the usual Josephson oscillations are strongly suppressed. In addition, we propose to modulate this tilted double well periodically in time, such that the individual wells are shifted sinusoidally up and down, in phase opposition to each other and with angular frequency ω, by an amount µ 1 . Such a modulation of an optical double well can be achieved by periodically shifting the focus of a blue-detuned laser, which creates the barrier between the two wells, with the help of a piezoactuated ...

show abstract

mentioning

confidence: 99%

mentioning

confidence: 99%

Analog of Photon-Assisted Tunneling in a Bose-Einstein Condensate

et al. 2005

Self Cite

View full text Add to dashboard Cite

show abstract

“…In the same way, we stipulate that the overlap of the functions u 1 (x) and u 2 (x) be only minute, which implies that the condensates in the two wells are merely weakly coupled, and ignore the high-order overlaps between two functions [33][34][35]. Then the interaction between atoms H int is given as…”

Section: Model Of Many-body Lz Processes In a Diagonal Periodic Dmentioning

confidence: 99%

“…The system under consideration is a gaseous BEC of bosonic atoms in a double-well potential [30][31][32][33][34][35], see its schematic diagrams in Fig. 1.…”

Section: Model Of Many-body Lz Processes In a Diagonal Periodic Dmentioning

confidence: 99%

See 1 more Smart Citation

Photon-induced sideband transitions in a many-body Landau-Zener process

et al. 2014

View full text Add to dashboard Cite

We investigate the many-body Landau-Zener (LZ) process in a two-site Bose-Hubbard model driven by a time-periodic field. We find that the driving field may induce sideband transitions in addition to the main LZ transitions. These photon-induced sideband transitions are a signature of the photon-assisted tunneling in our many-body LZ process. In the strong interaction regime, we develop an analytical theory for understanding the sideband transitions, which is confirmed by our numerical simulation. Furthermore, we discuss the quantization of the driving field. In the effective model of the quantized driving field, the sideband transitions can be understood as the LZ transitions between states of different "photon" numbers.

show abstract

Quantum tunneling of ultracold atoms in optical traps

et al. 2013

Front. Phys.

View full text Add to dashboard Cite

Many-particle tunnelling in a driven Bosonic Josephson junction

Cited by 37 publications

References 31 publications

Analog of Photon-Assisted Tunneling in a Bose-Einstein Condensate

Analog of Photon-Assisted Tunneling in a Bose-Einstein Condensate

Photon-induced sideband transitions in a many-body Landau-Zener process

Quantum tunneling of ultracold atoms in optical traps

Contact Info

Product

Resources

About