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arXiv:1103.3087 · Physical Review A

Enhancement of spin coherence in a spin-1 Bose-Einstein condensate by dynamical decoupling approaches

Bo‐Yuan Ning, Jun Zhuang, J. Q. You, Wenxian Zhang

Published Jul 18, 2011• 12 citations
arXivHTMLPDF

Abstract

We study the enhancement of spin coherence with periodic, concatenated, or Uhrig dynamical decoupling $N$-pulse sequences in a spin-1 Bose-Einstein condensate, where the intrinsic dynamical instability in such a ferromagnetically interacting condensate causes spin decoherence and eventually leads to a multiple spatial-domain structure or a spin texture. Our results show that all three sequences successfully enhance the spin coherence by pushing the wave vector of the most unstable mode in the condensate to a larger value. Among the three sequences with the same number of pulses, the concatenated one shows the best performance in preserving the spin coherence. More interestingly, we find that all three sequences exactly follow the same enhancement law, ${k}_{\ensuremath{-}}{T}^{1/2}=c$, with ${k}_{\ensuremath{-}}$ the wave vector of the most unstable mode, $T$ the sequence period, and $c$ a sequence-dependent constant. Such a law between ${k}_{\ensuremath{-}}$ and $T$ is also derived analytically for an attractive scalar Bose-Einstein condensate subjected to a periodic dynamical decoupling sequence.

DOI
10.1103/physreva.84.013606

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We study the enhancement of spin coherence with periodic, concatenated, or Uhrig dynamical decoupling NNN-pulse sequences in a spin-1 Bose-Einstein condensate, where the intrinsic dynamical instability in such a ferromagnetically interacting condensate causes spin decoherence and eventually leads to a multiple spatial-domain structure or a spin texture. Our results show that all three sequences successfully enhance the spin coherence by pushing the wave vector of the most unstable mode in the condensate to a larger value. Among the three sequences with the same number of pulses, the concatenated one shows the best performance in preserving the spin coherence. More interestingly, we find that all three sequences exactly follow the same enhancement law, k\ensuremath−T1/2=c{k}_{\ensuremath{-}}{T}^{1/2}=ck\ensuremath−​T1/2=c, with k\ensuremath−{k}_{\ensuremath{-}}k\ensuremath−​ the wave vector of the most unstable mode, TTT the sequence period, and ccc a sequence-dependent constant. Such a law between k\ensuremath−{k}_{\ensuremath{-}}k\ensuremath−​ and TTT is also derived analytically for an attractive scalar Bose-Einstein condensate subjected to a periodic dynamical decoupling sequence.
We investigate the feasibility for the preservation of coherence and entanglement of one- and two-spin qubits coupled to an interacting quantum spin-1/2 chain within the dynamical decoupling (DD) scheme. The performance is examined by counting the number of computing pulses that can be applied periodically with periods of TTT before qubits become decoherent, while an identical decoupling pulse sequence is applied within each cycle. By considering pulses with mixed directions and finite width controlled by magnetic fields, it is shown that pulse-width accumulation degrades the performance of sequences with larger numbers of pulses and that feasible magnetic fields in practice restrict consideration to sequences with few than 10 decoupling pulses within each cycle. Furthermore, within each cycle TTT, exact nontrivial pulse sequences are found to suppress the qubit-bath coupling to O(TN+1)O({T}^{N+1})O(TN+1) progressively with the minimum number of pulses being 4, 7, and 12 for N=1,2,3N=1,2,3N=1,2,3. These sequences, when applied to all qubits, are shown to preserve both the entanglement and coherence. Based on time-dependent density matrix renormalization, our numerical results show that for modest magnetic fields (10--40 T) available in laboratories, the overall performance is optimized when the number of pulses in each cycle is 4 or 7 with pulse directions alternating between xxx and zzz. Our results provide useful guides for the preservation of coherence and entanglement of spin qubits in the solid state.
It remains a challenge to independently manipulate the magnetic dipolar and the spin-exchange interactions, which are entangled in many spin systems, particularly in spin-1 Bose-Einstein condensates. For this purpose, we put forward a sequence of rf pulses and the periodic dynamical decoupling sequence of optical Feshbach resonance pulses to control the dipolar and the spin-exchange interactions, respectively. Our analytic results and the numerical simulations demonstrate that either of the two interactions can be suppressed to make the other dominate the spin dynamics; furthermore, both of the interactions can be simultaneously suppressed to realize spinor-condensate--based magnetometers with a higher sensitivity. This manipulation method may find its wide applications in magnetic resonance and spintronics.
We study the formation of transient Faraday patterns and spin textures in driven quasi-one-dimensional and quasi-two-dimensional spin-1 Bose-Einstein condensates under the periodic modulation of sss-wave scattering lengths a0a_0a0​ and a2a_2a2​, starting from the anti-ferromagnetic phase. This phase is characterized by a Bogoliubov spectrum consisting of three modes: one mode is gapped, while the other two are gapless. When a0a_0a0​ is modulated and half of the modulation frequency lies below the gapped mode, density and spin Faraday patterns emerge. In that case, in quasi-one-dimension, the spin texture is characterized by periodic domains of opposite zzz-polarizations. When driven above the gap, the spin texture is characterized by random orientations of spin vectors along the condensate axis. Qualitatively new features appear in the driven quasi-two-dimensional condensate. For instance, when driven above the gap, the spin textures are characterized by anomalous vortices and antivortices that do not exhibit phase winding in individual magnetic components. Below the gap, the spin texture exhibits irregular ferromagnetic patches with opposite polarizations. The spatial spin-spin correlations in quasi-one-dimension exhibit a Gaussian envelope, whereas they possess a Bessel function dependence in quasi-two-dimension. Under the a2a_2a2​-modulation, the density patterns dominate irrespective of the driving frequency, unless the spin-dependent interaction strength is sufficiently smaller than that of the spin-independent interaction. The intriguing scenario of competing instability can emerge when both scattering lengths are simultaneously modulated. Finally, we show that the competing instabilities result in a complex relationship between the population transfer and the strength of the quadratic Zeeman field, while keeping all other parameters constant.
We model the nonlinear behavior of spin-1 Bose-Einstein condensates (BECs) with repulsive spin-independent interactions and either ferromagnetic or antiferromagnetic (polar) spin-dependent interactions, loaded into a one-dimensional optical lattice potential. We show that both types of BECs exhibit dynamical instabilities and may form spatially localized multicomponent structures. The localized states of the spinor matter waves take the form of vector gap solitons and self-trapped waves that exist only within gaps of the linear Bloch-wave band-gap spectrum. Of special interest are the nonlinear localized states that do not exhibit a common spatial density profile shared by all condensate components, and consequently cannot be described by the single mode approximation (SMA) frequently employed within the framework of the mean-field treatment. We show that the non-SMA states can exhibits Josephson-like internal oscillations and self-magnetization, i.e., intrinsic precession of the local spin. Finally, we demonstrate that nonstationary states of a spinor BEC in a lattice exhibit coherent undamped spin-mixing dynamics, and that their controlled conversion into a stationary state can be achieved by the application of an external magnetic field.
We interpret the recently observed spatial domain formation in spin-1 atomic condensates as a result of dynamical instability. Within the mean field theory, a homogeneous condensate is dynamically unstable (stable) for ferromagnetic (antiferromagnetic) atomic interactions. We find that this dynamical instability naturally leads to spontaneous domain formation as observed in several recent experiments for condensates with rather small numbers of atoms. For trapped condensates, our numerical simulations compare quantitatively to the experimental results, thus largely confirming the physical insight from our analysis of the homogeneous case.
We analyze the formation of transient patterns and spin-spin correlations in quasi-two-dimensional spin-1 homogeneous Bose-Einstein condensates subjected to parametric driving of sss-wave scattering lengths. The dynamics for an initial ferromagnetic phase is identical to that of a scalar condensate. In contrast, intriguing dynamics emerges for an initial polar state. For instance, we show that competition exists between density patterns and spin-mixing dynamics. Dominant spin-mixing dynamics lead to a gas of polar core vortices and antivortices of different spin textures. The density modes of the Bogoliubov spectrum govern the wave-number selection of Faraday patterns. The spin modes determine the vortex density and the spatial dependence of spin-spin correlation functions. When the density patterns outgrow the spin-mixing dynamics, the spin-spin correlations decay exponentially with a correlation length of the order of a spin healing length; otherwise, they exhibit a Bessel function dependence. Strikingly, competing instabilities within density and spin modes emerge when both scattering lengths are modulated at different frequencies and appropriate modulation amplitudes. The competing instability leads to a superposition of density patterns or correlation functions of two distinct wavelengths. Our studies reveal that fine control over the driven dynamics can be attained by tuning interaction strengths, quadratic Zeeman field, driving frequencies, and amplitudes.