We perform nonperturbative analysis of forward scattering of resonance laser light on atoms in magnetic field when the laser drives transitions between states with total angular momenta F=1,2 and study the role of the induced higher-order multipole moments in the forward-scattering signal. It is shown how the multipole moments affect these signals and why not all possible multipoles are revealed for some transitions. The analysis is performed in terms of density-matrix formalism and in terms of coupled and uncoupled (trap) states. Evolution of the trap states in a magnetic field is found to be responsible for specific dependencies of the forward-scattering signals on the multipoles of various ranks. The general theory is applied to the case of the Na ${\mathit{D}}_{1}$ line. We also present a pump-probe method for studying multipoles in systems with states of high angular momenta and with complex transitions overlapping within their Doppler width. \textcopyright{} 1996 The American Physical Society.We perform nonperturbative analysis of forward scattering of resonance laser light on atoms in magnetic field when the laser drives transitions between states with total angular momenta F=1,2 and study the role of the induced higher-order multipole moments in the forward-scattering signal. It is shown how the multipole moments affect these signals and why not all possible multipoles are revealed for some transitions. The analysis is performed in terms of density-matrix formalism and in terms of coupled and uncoupled (trap) states. Evolution of the trap states in a magnetic field is found to be responsible for specific dependencies of the forward-scattering signals on the multipoles of various ranks. The general theory is applied to the case of the Na ${\mathit{D}}_{1}$ line. We also present a pump-probe method for studying multipoles in systems with states of high angular momenta and with complex transitions overlapping within their Doppler width. \textcopyright{} 1996 The American Physical Society.

Physical Review ASep 1, 199611 citations

Quantum phase transitions in an ion trap

Milburn

Quantum Electronics and Laser Science ConferenceJan 1, 20000 citations

Quantum Phase Transitions in a Linear Ion Trap

Gerard J Milburn, Paul M. Alsing

arXiv:quant-ph/0003001Springer eBooksNov 16, 20074 citations

Correcting symmetry imperfections in linear multipole traps

J. Pedregosa-Gutierrez, C. Champenois, M. Houssin +2 more

Multipole radio-frequency (RF) traps are central to collisional experiments in cryogenic environments. They also offer possibilities to generate new type of ion crystals topologies and in particular the potential to create infinite 1D/2D structures: ion rings and ion tubes. However, multipole traps have also been shown to be very sensitive to geometrical misalignment of the trap rods, leading to additional local trapping minima. The present work proposes a method to correct non-ideal potentials, by modifying the applied RF amplitudes for each trap rod. This approach is discussed for the octupole trap, leading to the restitution of the ideal Mexican-Hat-like pseudo-potential, expected in multipole traps. The goodness of the compensation method is quantified in terms of the choice of the diagnosis area, the residual trapping potential variations, the required adaptation of the applied RF voltage amplitudes, and the impact on the trapped ion structures. Experimental implementation for macroscopic multipole traps is also discussed, in order to propose a diagnostic method with respect to the resolution and stability of the trap drive. Using the proposed compensation technique, we discuss the feasibility of generating a homogeneous ion ring crystal, which is a measure of quality for the obtained potential well.Multipole radio-frequency (RF) traps are central to collisional experiments in cryogenic environments. They also offer possibilities to generate new type of ion crystals topologies and in particular the potential to create infinite 1D/2D structures: ion rings and ion tubes. However, multipole traps have also been shown to be very sensitive to geometrical misalignment of the trap rods, leading to additional local trapping minima. The present work proposes a method to correct non-ideal potentials, by modifying the applied RF amplitudes for each trap rod. This approach is discussed for the octupole trap, leading to the restitution of the ideal Mexican-Hat-like pseudo-potential, expected in multipole traps. The goodness of the compensation method is quantified in terms of the choice of the diagnosis area, the residual trapping potential variations, the required adaptation of the applied RF voltage amplitudes, and the impact on the trapped ion structures. Experimental implementation for macroscopic multipole traps is also discussed, in order to propose a diagnostic method with respect to the resolution and stability of the trap drive. Using the proposed compensation technique, we discuss the feasibility of generating a homogeneous ion ring crystal, which is a measure of quality for the obtained potential well.

arXiv:1807.10500Review of Scientific InstrumentsDec 1, 20187 citations

Controlling the stability of nonlinear optical modes via electromagnetically induced transparency

Kun Zhang, Yi-zeng Liang, Ji Lin +1 more

We propose a scheme to generate and stabilize the high-dimensional spatial solitons via electromagnetically induced transparency (EIT). The system we consider is a resonant atomic ensemble having $\mathrm{\ensuremath{\Lambda}}$ configuration. We illustrate that under EIT conditions the equation satisfied by the probe field envelope is reduced to a saturable nonlinear Schr\"odinger equation with the trapping potential, provided by a far-detuned laser field and a random magnetic field. We present high-dimensional soliton solutions exhibiting many interesting characteristics, including diversity (i.e., many different types of soliton solutions can be found, including bright, ring multipole bright, ring multipole defect mode, multiring bright, multiring defect mode, and vortices solitons), the phase transition between bright soliton and higher-order defect modes (i.e., the phase transition can be realized by controlling the nonlinear coefficient or the intensity of the trapping potential), and stability (i.e., various solitons can be stabilized by the Gaussian potential provided by the far detuned laser field, or the random potential provided by the magnetic field). We also find that some solitons are the extension of the linear eigenmode, whereas others entirely derive from the role of nonlinearity. Compared with previous studies, we not only show the diverse soliton solutions in the same system but also find the boundary of the phase transition for the type of solitons. In addition, we present the possibility of using the random potential to stabilize various solitons and vortices.We propose a scheme to generate and stabilize the high-dimensional spatial solitons via electromagnetically induced transparency (EIT). The system we consider is a resonant atomic ensemble having $\mathrm{\ensuremath{\Lambda}}$ configuration. We illustrate that under EIT conditions the equation satisfied by the probe field envelope is reduced to a saturable nonlinear Schr\"odinger equation with the trapping potential, provided by a far-detuned laser field and a random magnetic field. We present high-dimensional soliton solutions exhibiting many interesting characteristics, including diversity (i.e., many different types of soliton solutions can be found, including bright, ring multipole bright, ring multipole defect mode, multiring bright, multiring defect mode, and vortices solitons), the phase transition between bright soliton and higher-order defect modes (i.e., the phase transition can be realized by controlling the nonlinear coefficient or the intensity of the trapping potential), and stability (i.e., various solitons can be stabilized by the Gaussian potential provided by the far detuned laser field, or the random potential provided by the magnetic field). We also find that some solitons are the extension of the linear eigenmode, whereas others entirely derive from the role of nonlinearity. Compared with previous studies, we not only show the diverse soliton solutions in the same system but also find the boundary of the phase transition for the type of solitons. In addition, we present the possibility of using the random potential to stabilize various solitons and vortices.

Physical Review AFeb 27, 201813 citations

{\mathit{D}}_{1}

line. We also present a pump-probe method for studying multipoles in systems with states of high angular momenta and with complex transitions overlapping within their Doppler width. \textcopyright{} 1996 The American Physical Society.