Proliferation of atomic wave packets at the nodes of a standing light wave

A quantum analysis is presented of the motion and internal state of a two-level atom in a strong standing-wave light field. Coherent evolution of the atomic wave-packet, atomic dipole moment, and population inversion strongly depends on the ratio between the detuning from atom-field resonance and a characteristic atomic frequency. In the basis of dressed states, atomic motion is represented as wave-packet motion in two effective optical potentials. At exact resonance, coherent population trapping is observed when an atom with zero momentum is centered at a standing-wave node. When the detuning is comparable to the characteristic atomic frequency, the atom crossing a node may or may not undergo a transition between the potentials with probabilities that are similar in order of magnitude. In this detuning range, atomic wave packets proliferate at the nodes of the standing wave. This phenomenon is interpreted as a quantum manifestation of chaotic transport of classical atoms observed in earlier studies. For a certain detuning range, there exists an interval of initial momentum values such that the atom simultaneously oscillates in an optical potential well and moves as a ballistic particle. This behavior of a wave packet is a quantum analog of a classical random walk of an atom, when it enters and leaves optical potential wells in a seemingly irregular manner and freely moves both ways in a periodic standing light wave. In a far-detuned field, the transition probability between the potentials is low, and adiabatic wave-packet evolution corresponding to regular classical motion of an atom is observed.     

Hamiltonian Ratchets with Ultra‐Cold Atoms

Quantum‐resonance ratchets have been realized over the last ten years for the production of directed currents of atoms. These non‐dissipative systems are based on the interaction of a Bose‐Einstein condensate with an optical standing wave potential to produce a current of atoms in momentum space. In this paper we provide a review of the important features of these ratchets with a particular emphasis on their optimization using more complex initial states. We also examine their stability close to resonance conditions of the kicking. Finally we discuss the way in which these ratchets may pave the way for applications in quantum (random) walks and matter‐wave interferometry.     

Quantum Signatures of Chaos in Adiabatic Interaction Between a Trapped Ion and a Laser Standing Wave

We study quantum motion around a classical heteroclinic point of a single trapped ion interacting with a strong laser standing wave. We construct a set of exact coherent states of the quantum system and from the exact solutions reveal that quantum signatures of chaos can be induced by the adiabatic interaction between the trapped ion and the laser standing wave, where the quantum expectation values of position and momentum correspond to the classically chaotic orbit. The chaotic region on the phase space is illustrated. The energy crossing and quantum resonance in time evolution and the exponentially increased Heisenberg uncertainty are found. The results suggest a theoretical scheme for controlling the unstable regular and chaotic motions.     

Coherent control of ballistic energy growth for a kicked Bose-Einstein condensate

We consider a Bose-Einstein condensate which is split into two momentum components and then “kicked" at the Talbot time by an optical standing wave. The mean energy growth is shown to be suppressed or enhanced depending on the quantum phase between the two momentum components. Experimental verification is provided and we discuss possible implications of our results for recently suggested applications of kicked atoms.     

Quantum magnetism with multicomponent dipolar molecules in an optical lattice

We consider bosonic dipolar molecules in an optical lattice prepared in a mixture of different rotational states. The 1/R(3) interaction between molecules for this system is produced by exchanging a quantum of angular momentum between two molecules. We show that the Mott states of such systems have a large variety of quantum phases characterized by dipolar orderings including a state with an ordering wave vector that can be changed by tilting the lattice. As the Mott insulating phase is melted, we also describe several exotic superfluid phases that will occur.     

Quantum carpets woven by cold atoms in a laser field

Propagation of wave packets of cold two-level atoms in a standing-wave laser field can be interpreted in the dressed-state basis as motion in two optical potentials. The three distinct regimes of the wavepacket motion are specified by the ratio of the squared atom–laser detuning to the normalized Doppler shift. We calculate the momentum and position probability densities, which form patterns with minima and maxima of probability both in the momentum and the position spaces known as quantum carpets. At small and large detunings, the atomic motion is substantially adiabatic, and the quantum carpets have a simple form. At intermediate detunings, the wave packet moves nonadiabatically, splitting at each node of the standing wave, which causes a proliferation or branching of atomic trajectories with a single atom. Nonadiabatic transitions produce beautiful quantum carpets with a rich structure.     

无限深势阱中粒子的态密度

对于自由粒子在有限容器中的能态密度,热力学统计教材一般根据半经典量子图像,由驻波条件和德布罗意关系,以动量分立值为基础出发得到;然而根据量子理论,无限深势阱中的粒子存在能量本征态,而非动量本征态.本文以能量本征态为统计对象推导了有限体积中的自由粒子的能态密度,结果与教材一致.但是我们的处理方式显得更为自然.     

Exploring the phase space of the quantum delta-kicked accelerator

We experimentally explore the underlying pseudoclassical phase space structure of the quantum delta-kicked accelerator. This was achieved by exposing a Bose-Einstein condensate to the spatially corrugated potential created by pulses of an off-resonant standing light wave. For the first time quantum accelerator modes were realized in such a system. By utilizing the narrow momentum distribution of the condensate we were able to observe the discrete momentum state structure of a quantum accelerator mode and also to directly measure the size of the structures in the phase space.     

Optical control of the rotational angular momentum of a molecular Rydberg wave packet

An intuitive scheme for controlling the rotational quantum state of a Rydberg molecule is demonstrated experimentally. We determine the accumulated phase difference between the various components of a molecular electron wave packet, and then employ a sequence of phase-locked optical pulses to selectively enhance or depopulate specific rotational states. The angular momentum composition of the resulting wave packet, and the efficiency of the control scheme, is determined by calculating the multipulse response of the time-dependent Rydberg populations.     

Observation of high-order quantum resonances in the kicked rotor

Quantum resonances in the kicked rotor are characterized by a dramatically increased energy absorption rate, in stark contrast to the momentum localization generally observed. These resonances occur when the scaled Planck's constant Planck's [over ]=r/s 4pi, for any integers r and s. However, only the variant Planck's [over ]=r2pi resonances are easily observable. We have observed high-order quantum resonances (s>2) utilizing a sample of low energy, noncondensed atoms and a pulsed optical standing wave. Resonances are observed for variant Planck's [over ]=r/16 4pi for integers r=2-6. Quantum numerical simulations suggest that our observation of high-order resonances indicate a larger coherence length (i.e., coherence between different wells) than expected from an initially thermal atomic sample.     

Anomalous spatial concentration of atoms in the field of a standing light wave

The stationary momentum and coordinate distributions of two-level atoms in the field of a one-dimensional standing light wave have been studied. A qualitatively new effect—the predominant concentration of atoms outside of the minima of the optical potential—has been detected in the regime of moderate saturation of an atomic transition and red frequency detuning. This effect has been qualitatively interpreted. Calculations have been performed using the quantum kinetic equation for the atomic density matrix with the complete inclusion of recoil and localization effects in an arbitrary-intensity light field. In addition to theoretical significance, the results can be useful for atomic nanolithography and frequency standards based on optical gratings.     

无限深势阱中单粒子的泡利处理

Pauli在处理无限深势阱中的单粒子时,要求粒子具有经典力学的能量动量关系E=p²/2m,而且混用了定波和定态的概念,这说明Pauli更多地用到的是半经典量子论而不是量子力学,他所得到的动量分布函数是半经典理论的结果,只有在大量子数极限下才与量子力学的结果趋于一致.     

High-order quantum resonances observed in a periodically kicked Bose-Einstein condensate

We have observed high-order quantum resonances in a realization of the quantum delta-kicked rotor, using Bose-condensed Na atoms subjected to a pulsed standing wave of laser light. These resonances occur for pulse intervals that are rational fractions of the Talbot time, and are characterized by ballistic momentum transfer to the atoms. The condensate's narrow momentum distribution not only permits the observation of the quantum resonances at 3/4 and 1/3 of the Talbot time, but also allows us to study scaling laws for the resonance width in quasimomentum and pulse interval.     

Atomic localization caused by the asymmetry of the Landau-Zener transitions

The motion of an atomic wave packet in a standing light wave can be described in terms of two periodic potentials. Single atom may perform Landau-Zener (LZ) transitions between these two energy states. In this Letter we have found regimes when atom is localized in the momentum space in the vicinity of its initial momentum. We argue that this localization is caused by the asymmetry of LZ transitions (i.e. probability of tunneling depends on its direction) due to the interference.     

Scattering from a PT symmetric standing wave

We study the Kapitza–Dirac diffraction of a free beam particle in the presence of a PT symmetric standing wave. We discuss that the momentum and total probability are not conserved in the non-Hermitian scattering process. We show that the average momentum gain/loss does not vanish over a period even if the non-Hermitian optical potential changes periodically in time. We give the resonance conditions at which large momentum transfer is produced.     

Relativistic quantum correlations in bipartite fermionic states

The influences of relative motion, the size of the wave packet and the average momentum of the particles on different types of correlations present in bipartite quantum states are investigated. In particular, the dynamics of the quantum mutual information, the classical correlation and the quantum discord on the spin correlations of entangled fermions are studied. In the limit of small average momentum, regardless of the size of the wave packet and the rapidity, the classical and the quantum correlations are equally weighted. On the other hand, in the limit of large average momentum, the only correlations that exist in the system are the quantum correlations. For every value of the average momentum, the quantum correlations maximize at an optimal size of the wave packet. It is shown that after reaching a minimum value, the revival of quantum discord occurs with increasing rapidity.     

Observing the phase space trajectory of an entangled matter wave packet

We observe the phase space trajectory of an entangled wave packet of a trapped ion with high precision. The application of a spin-dependent light force on a superposition of spin states allows for coherent splitting of the matter wave packet such that two distinct components in phase space emerge. We observe such motion with a precision of better than 9% of the wave packet extension in both momentum and position, corresponding to a 0.8 nm position resolution. We accurately study the effect of the initial ion temperature on the quantum entanglement dynamics. Furthermore, we map out the phonon distributions throughout the action of the displacement force. Our investigation shows corrections to simplified models of the system evolution. The precise knowledge of these dynamics may improve quantum gates for ion crystals and lead to entangled matter wave states with large displacements.     

Coherent transport of neutral atoms in spin-dependent optical lattice potentials

We demonstrate the controlled coherent transport and splitting of atomic wave packets in spin-dependent optical lattice potentials. Such experiments open intriguing possibilities for quantum state engineering of many body states. After first preparing localized atomic wave functions in an optical lattice through a Mott insulating phase, we place each atom in a superposition of two internal spin states. Then state selective optical potentials are used to split the wave function of a single atom and transport the corresponding wave packets in two opposite directions. Coherence between the wave packets of an atom delocalized over up to seven lattice sites is demonstrated.     

Interpretation of the Quantum Measurement: Example of a Linearly Coupled Harmonic Oscillator

We argue that it may be possible to consistently explain the quantum measurement by assuming that the wave function is in one-to-one correspondence with objective physical reality and has no probabilistic interpretation. In the context of such approach we consider the model of a harmonic oscillator linearly coupled to a heat bath and treat the oscillator as the system being measured. Three classes of initial pure states for the bath are considered. Exact expressions for the average values and variances of the oscillator coordinate and momentum as functions of time are considered for each class of pure states. It is shown that these quantities exhibit different asymptotic behavior for different classes of initial states of the bath. In particular, if each mode of the bath is initially in a coherent state, then for an arbitrary initial state of the oscillator the variances of the oscillator coordinate and momentum asymptotically approach the same values as for a coherent state of the free oscillator, while the averages of coordinate and momentum show a Brownian-like behavior. We argue that such behavior shows several features of the quantum measurement and supports our interpretation of the wave function.     

High-efficiency detection of a single quantum of angular momentum by suppression of optical pumping

We propose and demonstrate experimentally the discrimination between two spin states of an atom purely on the basis of their angular momentum. The discrimination relies on angular momentum selection rules and does not require magnetic effects such as a magnetic dipole moment of the atom or an applied magnetic field. The central ingredient is to prevent by coherent population trapping an optical pumping process which would otherwise relax the spin state before a detectable signal could be obtained. We detected the presence or absence of a single quantum (h) of angular momentum in a trapped calcium ion in a single observation with success probability 0.86. As a practical technique, the method can be applied to read out some types of quantum computer.