We report on the collapse and revival of Ramsey fringe visibility when a spatially dependent phase is imprinted in the coherences of a trapped ensemble of two-level atoms. The phase is imprinted via the light shift from a Gaussian laser beam which couples the dynamics of internal and external degrees of freedom for the atoms in an echo spectroscopy sequence. The observed revivals are directly linked to the oscillatory motion of atoms in the trap. An understanding of the effect is important for quantum state engineering of trapped atoms.
We experimentally demonstrate and systematically study the stimulated revival (echo) of motional wave packet oscillations. For this purpose, we prepare wave packets in an optical lattice by non-adiabatically shifting the potential and stimulate their reoccurence by a second shift after a variable time delay. This technique, analogous to spin echoes, enables one even in the presence of strong dephasing to determine the coherence time of the wave packets. We find that for strongly bound atoms it is comparable to the cooling time and much longer than the inverse of the photon scattering rate.
We investigate the dephasing of ultra cold ^{85}Rb atoms trapped in an optical dipole trap and prepared in a coherent superposition of their two hyperfine ground states by interaction with a microwave pulse. We demonstrate that the dephasing, measured as the Ramsey fringe contrast, can be reversed by stimulating a coherence echo with a pi-pulse between the two pi/2 pulses, in analogy to the photon echo. We also demonstrate that the failure of the echo for certain trap parameters is due to dynamics in the trap, and thereby that ''echo spectroscopy'' can be used to study the quantum dynamics in …
We investigate the coherence properties of thermal atoms confined in optical dipole traps where the underlying classical dynamics is chaotic. A perturbative expression derived for the coherence of the echo scheme of [Andersen et. al., Phys. Rev. Lett. 90, 023001 (2003)] shows it is a function of the survival probability or fidelity of eigenstates of the motion of the atoms in the trap. The echo coherence and the survival probability display "system specific" features, even when the underlying classical dynamics is chaotic. In particular, partial revivals in the echo signal and the survival pro…
We report observations of Ramsey interferences and spin echoes from electron spins inside a levitating macroscopic particle. The experiment is realized using nitrogen-vacancy (NV) centers hosted in a micron-sized diamond stored in a Paul trap both under atmospheric conditions and under vacuum. Spin echoes are used to show that the Paul trap preserves the coherence time of the embedded electron spins for more than microseconds. Conversely, the NV spin is employed to demonstrate high angular stability of the diamond even under vacuum. These results are significant steps towards strong coupling o…
I show how to perform a Loschmidt echo (time reversal) in the Bose-Hubbard model implemented with cold bosonic atoms in an optical lattice. The echo is obtained by applying a linear phase imprint on the lattice and a change in magnetic field to tune the boson-boson scattering length through a Feshbach resonance. I discuss how the echo can measure the fidelity of the quantum simulation, the intensity of an external potential (e.g. gravity), or the critical point of the superfluid-insulator quantum phase transition.
We discuss a recently demonstrated type of microwave spectroscopy of trapped ultra-cold atoms known as "echo spectroscopy" [M.F. Andersen et. al., Phys. Rev. Lett., in press (2002)]. Echo spectroscopy can serve as an extremely sensitive experimental tool for investigating quantum dynamics of trapped atoms even when a large number of states are thermally populated. We show numerical results for the stability of eigenstates of an atom-optics billiard of the Bunimovich type, and discuss its behavior under different types of perturbations. Finally, we propose to use special geometrical constructio…
We present a scheme for eliminating the optical diffraction of slow-light in a thermal atomic medium of electromagnetically induced transparency. Nondiffraction is achieved for an arbitrary paraxial image by manipulating the susceptibility in momentum space, in contrast to the common approach, which employs guidance of specific modes by manipulating the susceptibility in real space. For negative two-photon detuning, the moving atoms drag the transverse momentum components unequally, resulting in a Doppler trapping of light by atoms in two dimensions.
When ground state atoms are excited to a Rydberg state, van der Waals interactions among them can lead to a strong suppression of the excitation. Despite the strong interactions the evolution can still be reversed by a simple phase shift in the excitation laser field. We experimentally prove the coherence of the excitation in the strong blockade regime by applying an `optical rotary echo' technique to a sample of magnetically trapped ultracold atoms, analogous to a method known from nuclear magnetic resonance. We additionally measured the dephasing time due to the interaction between the Rydbe…
A quantum phase transition is generally thought to imprint distinctive characteristics on the nonequilibrium dynamics of a closed quantum system. Specifically, the Loschmidt echo after a sudden quench to a quantum critical point $-$ measuring the time dependence of the overlap between initial and time-evolved states $-$ is expected to exhibit an accelerated relaxation followed by periodic revivals. We here introduce a new exactly solvable model, the extended Su-Schrieffer-Heeger model, the Loschmidt echo of which provides a counterexample. A parallell analysis of the quench dynamics of the thr…
We perform echo spectroscopy on ultra cold atoms in atom optics billiards, to study their quantum dynamics. The detuning of the trapping laser is used to change the ``perturbation'', which causes a decay in the echo coherence. Two different regimes are observed: First, a perturbative regime in which the decay of echo coherence is non-monotonic and partial revivals of coherence are observed. These revivals are more pronounced in traps with mixed dynamics as compared to traps where the dynamics is fully chaotic. Next, for stronger perturbations, the decay becomes monotonic and independent of the…
Quantum interferometers are generally set so that phase differences between paths in coordinate space combine constructive or destructively. Indeed, the interfering paths can also meet in momentum space leading to momentum-space fringes. We propose and analyze a method to produce interference in momentum space by phase-imprinting part of a trapped atomic cloud with a detuned laser. For one-particle wave functions analytical expressions are found for the fringe width and shift versus the phase imprinted. The effects of unsharpness or displacement of the phase jump are also studied, as well as m…
Transverse spin diffusion in a polarized, interacting Fermi gas leads to the Leggett-Rice effect, where the spin current precesses around the local magnetization. With a spin-echo sequence both the transverse diffusivity and the spin-rotation parameter $γ$ are obtained; the sign of $γ$ reveals the repulsive or attractive character of the effective interaction. In a trapped Fermi gas the spin diffusion equations become nonlinear, and their numerical solution exhibits an inhomogeneous spin state even at the spin echo time. While the microscopic diffusivity and $γ$ increase at weak coupling, thei…
The evanescent field outside an optical nanofiber (ONF) can create optical traps for neutral atoms. We present a non-destructive method to characterize such trapping potentials. An off-resonance linearly polarized probe beam that propagates through the ONF experiences a slow axis of polarization produced by trapped atoms on opposite sides along the ONF. The transverse atomic motion is imprinted onto the probe polarization through the changing atomic index of of refraction. By applying a transient impulse, we measure a time-dependent polarization rotation of the probe beam that provides both a …
We study echoes and what we call 'revival echoes' for a collection of atoms that are described by a single quantum wavefunction and are confined in a weakly anharmonic trap. The echoes and revival echoes are induced by applying two, successive temporally localized potential perturbations to the confining potential, one at time $t=0$, and a smaller one at time $t=τ$. Pulse-like responses in the expectation value of position $<x(t)>$ are predicted at $t \approx nτ$ ($n=2,3,...$) and are particularly evident at $t \approx 2τ$. A novel result of our study is the finding of 'revival echoes'. Reviva…
The quantum coherence of a Bose-Einstein condensate is studied using the concept of quantum fidelity (Loschmidt echo). The condensate is confined in an elongated anharmonic trap and subjected to a small random potential such as that created by a laser speckle. Numerical experiments show that the quantum fidelity stays constant until a critical time, after which it drops abruptly over a single trap oscillation period. The critical time depends logarithmically on the number of condensed atoms and on the perturbation amplitude. This behavior may be observable by measuring the interference fringes…
We demonstrate the initialisation, read-out and high-speed manipulation of a qubit stored in a single 87 Rb atom trapped in a submicron-size optical tweezer. Single qubit rotations are performed on a sub-100 ns time scale using two-photon Raman transitions. Using the ``spin-echo'' technique, we measure an irreversible dephasing time of 34 ms. The read-out of the single atom qubit is at the quantum projection noise limit when averaging up to 1000 individual events.
Dense array of ions in microfabricated traps represent one possible way to scale up ion trap quantum computing. The ability to address individual ions is an important component of such a scheme. We demonstrate individual addressing of trapped ions in a microfabricated surface-electrode trap using a magnetic field gradient generated on-chip. A frequency splitting of 310(2) kHz for two ions separated by 5 um is achieved. Selective single qubit operations are performed on one of two trapped ions with an average of 2.2+/-1.0% crosstalk. Coherence time as measured by the spin-echo technique is unaf…
The orbital angular momentum (OAM) from a laser beam can be coherently transferred to a Bose-Einstein condensate in a ring trap, in quantized units of $\hbar$. The light-matter coupling allows for the superradiant transfer of the atoms between the discrete OAM states. Tuning the ring parameters and winding number of the pump light, specific angular momentum states can be populated. This in turn allows control of the emission to generate light with OAM different from that of the pump, as the atomic ring imprints its contribution on the scattered light.
We consider quantum gates for trapped ions using state-selective displacement of the ions. We generalize earlier work in order to treat arbitrary separations between the traps. This requires the impact of anharmonicity arising from the Coulomb interaction to be estimated. We show that its effects are always small enough to allow high fidelity. In particular, the method can be applied to two ions in the same trap. We also show that gates between non-neighbour ions, and hence a Toffoli (three-qubit controlled-NOT) gate, can be achieved. We discuss how the gate can be applied to logical qubits en…
We study in detail the mechanisms causing dephasing of hyperfine coherences of cesium atoms confined by a far off-resonant standing wave optical dipole trap [S. Kuhr et al., Phys. Rev. Lett. 91, 213002 (2003)]. Using Ramsey spectroscopy and spin echo techniques, we measure the reversible and irreversible dephasing times of the ground state coherences. We present an analytical model to interpret the experimental data and identify the homogeneous and inhomogeneous dephasing mechanisms. Our scheme to prepare and detect the atomic hyperfine state is applied at the level of a single atom as well as…
We discuss the dynamical behavior of the entanglement between the internal and the external degrees of freedom of a trapped atom in electromagnetically-induced transparency (EIT) laser cooling. It is shown that essential features of the intricate entanglement dynamics observed in full numerical simulations of the underlying quantum master equation can be understood in terms of a two-state model on the basis of Landau-Zener splittings in the atom-laser field Hamiltonian. An extension of this model to an effective non-Hermitian Hamiltonian is constructed which describes the decay of entanglement…
Ultra-cold atoms trapped in an optical dipole trap and prepared in a coherent superposition of their hyperfine ground states, decohere as they interact with their environment. We demonstrate than the loss in coherence in an "echo" experiment, which is caused by mechanisms such as Rayleigh scattering, can be suppressed by the use of a new pulse sequence. We also show that the coherence time is then limited by mixing to other vibrational levels in the trap and by the finite lifetime of the internal quantum states of the atoms.
We experimentally demonstrate the coherent manipulation of atomic states in far-detuned dipole traps and registers of dipole traps based on two-dimensional arrays of microlenses. By applying Rabi, Ramsey, and spin-echo techniques, we systematically investigate the dephasing mechanisms and determine the coherence time. Simultaneous Ramsey measurements in up to 16 dipole traps are performed and proves the scalability of our approach. This represents an important step in the application of scalable registers of atomic qubits for quantum information processing. In addition, this system can serve a…
We theoretically study an impulsively excited quantum bouncer (QB) - a particle bouncing off a surface in the presence of gravity. A pair of time-delayed pulsed excitations is shown to induce a wave-packet echo effect - a partial rephasing of the QB wave function appearing at twice the delay between pulses. In addition, an appropriately chosen observable [here, the population of the ground gravitational quantum state (GQS)] recorded as a function of the delay is shown to contain the transition frequencies between the GQSs, their populations, and partial phase information about the wave packet …
Quantum memories are an integral component of quantum repeaters - devices that will allow the extension of quantum key distribution to communication ranges beyond that permissible by passive transmission. A quantum memory for this application needs to be highly efficient and have coherence times approaching a millisecond. Here we report on work towards this goal, with the development of a $^{87}$Rb magneto-optical trap with a peak optical depth of 1000 for the D2 $F=2 \rightarrow F'=3$ transition using spatial and temporal dark spots. With this purpose-built cold atomic ensemble to implement t…
We experimentally study the ground state coherence properties of cesium atoms in a nanofiber-based two-color dipole trap, localized 200 nm away from the fiber surface. Using microwave radiation to coherently drive the clock transition, we record Ramsey fringes as well as spin echo signals and infer a reversible dephasing time $T_2^\ast=0.6$ ms and an irreversible dephasing time $T_2^\prime=3.7$ ms. By theoretically modelling the signals, we find that, for our experimental parameters, $T_2^\ast$ and $T_2^\prime$ are limited by the finite initial temperature of the atomic ensemble and the heatin…
The coherent population trapping (CPT) effect is used for making compact atomic clocks. There are two types of CPT clocks: the one in which the Raman beams are applied continuously and the one in which two CPT pulses separated by a dark period are applied (Ramsey scheme). It is obvious that the technique of spin squeezing can only be applied to the Ramsey CPT clock to enhance the sensitivity. However, it is not apparent how to adapt to the CPT clock the protocols for the microwave clock using one-axis-twist squeezing (OATS), since the Ramsey CPT clock is not trivially equivalent to the Ramsey …
We experimentally demonstrate the strong suppression of dephasing of a qubit stored in a single \textsuperscript{87}Rb atom in an optical dipole trap by using Carr-Purcell-Meiboom-Gill(CPMG) pulse sequences. Regarded as a repetition of spin echo, CPMG sequence is an optimal choice for suppressing both inhomogeneous and homogeneous phase decoherence mechanisms. In the trap with 830 nm wavelength and 0.7 mK potential depth, the spin relaxation time of single atoms is showed to be 830.8 ms. We obtain the reversible inhomogeneous dephasing time of $T_{2}^{\ast}$=1.4 ms. The homogeneous dephasing t…
We demonstrate single-atom trapping in two-dimensional arrays of microtraps with arbitrary geometries. We generate the arrays using a Spatial Light Modulator (SLM), with which we imprint an appropriate phase pattern on an optical dipole trap beam prior to focusing. We trap single $^{87}{\rm Rb}$ atoms in the sites of arrays containing up to $\sim100$ microtraps separated by distances as small as $3\;μ$m, with complex structures such as triangular, honeycomb or kagome lattices. Using a closed-loop optimization of the uniformity of the trap depths ensures that all trapping sites are equivalent. …
We study the suppression of noise-induced phase decoherence in a single atomic qubit by employing pulse sequences. The atomic qubit is composed of a single neutral atom in a far-detuned optical dipole trap and the phase decoherence may originate from the laser intensity and beam pointing fluctuations as well as magnetic field fluctuations. We show that suitable pulse sequences may prolongate the qubit coherence time substantially as comparing to the conventional spin echo pulse.
The "pushing gate" proposed by Cirac and Zoller in 2000 for quantum logic in ion traps is discussed, in which a force is used to give a controlled push to a pair of trapped ions and thus realize a phase gate. The original proposal had a weakness in that it involved a hidden extreme sensitivity to the size of the force. Also, the physical origin of this force was not fully addressed. Here, we discuss the sensitivity and present a way to avoid it by choosing the spatial form of the pushing force in an optimal way. We also analyse the effect of imperfections in a pair of pi pulses which are used …
The burgeoning fields of quantum computing and quantum key distribution have created a demand for a quantum memory. The gradient echo memory scheme is a quantum memory candidate for light storage that can boast efficiencies approaching unity, as well as the flexibility to work with either two or three level atoms. The key to this scheme is the frequency gradient that is placed across the memory. Currently the three level implementation uses a Zeeman gradient and warm atoms. In this paper we model a new gradient creation mechanism - the ac Stark effect - to provide an improvement in the flexibi…
Using a numerical implementation of the truncated Wigner approximation, we simulate the experiment reported by Ramanathan et al. in Phys. Rev. Lett. 106, 130401 (2011), in which a Bose-Einstein condensate is created in a toroidal trap and set into rotation via a phase imprinting technique. A potential barrier is then placed in the trap to study the decay of the superflow. We find that the current decays via thermally activated phase slips, which can also be visualized as vortices crossing the barrier region in the radial direction. Adopting the notion of critical velocity used in the experimen…
We numerically study the impact of Gaussian barrier height and width on the gray solitons population in a symmetric and asymmetric potential trap. The gray solitons are created in a double-well potential by the density engineering method. Two identical Bose-Einstein condensate fragments are confined and made to collide by switching off the Gaussian barrier in a double-well potential. We find that the gray solitons population can be manipulated by Gaussian barrier height and width. We also study the gray solitons population dependence on the coupling strength. Moreover, we also study the impact…
We investigate a method for generating nonlinear phase shifts on superpositions of photon number states. The light is stored in a Bose-Einstein condensate via electromagnetically-induced transparency memory techniques. The atomic collisions are exploited to generate a nonlinear phase shift of the stored state. The stored light is then revived with the nonlinear phase shift imprinted upon it. We show that this method can be used as a nonlinear-sign gate in the regime where the Thomas-Fermi and mean-field approximations are valid. We test these approximations using realistic parameters and find …
We propose to apply atom-chip techniques to the trapping of a single atom in a circular Rydberg state. The small size of microfabricated structures will allow for trap geometries with microwave cut-off frequencies high enough to inhibit the spontaneous emission of the Rydberg atom, paving the way to complete control of both external and internal degrees of freedom over very long times. Trapping is achieved using carefully designed electric fields, created by a simple pattern of electrodes. We show that it is possible to excite, and then trap, one and only one Rydberg atom from a cloud of groun…
Rapidly scanning magnetic and optical dipole traps have been widely utilised to form time-averaged potentials for ultracold quantum gas experiments. Here we theoretically and experimentally characterise the dynamic properties of Bose-Einstein condensates in ring-shaped potentials that are formed by scanning an optical dipole beam in a circular trajectory. We find that unidirectional scanning leads to a non-trivial phase profile of the condensate that can be approximated analytically using the concept of phase imprinting. While the phase profile is not accessible through in-trap imaging, time-o…
Non-vanishing fluctuations of the vacuum state are a salient feature of quantum theory. These fluctuations fundamentally limit the precision of quantum sensors. Nowadays, several systems such as optical clocks, gravitational wave detectors, matter-wave interferometers, magnetometers, and optomechanical systems approach measurement sensitivities where the effect of quantum fluctuations sets a fundamental limit, the so-called standard quantum limit (SQL). It has been proposed that the SQL can be overcome by squeezing the vacuum fluctuations. Realizations of this scheme have been demonstrated in …
