Numerically we simulate the effect of optimized coherent control pulses with a finite duration on a qubit in a bath of spins. The pulses of finite duration are compared with ideal instantaneous pulses. In particular, we show that properly designed short pulses can approximate ideal instantaneous pulses up to a certain order in the shortness of the pulse. We provide examples of such pulses, quantify the discrepancy from the ideal case and compare their effect for various ranges of the coupling constants.
We generalize the problem of the coherent control of small quantum systems to the case where the quantum bit (qubit) is subject to a fully general rotation. Following the ideas developed in Pasini et al (2008 Phys. Rev. A 77, 032315), the systematic expansion in the shortness of the pulse is extended to the case where the pulse acts on the qubit as a general rotation around an axis of rotation varying in time. The leading and the next-leading corrections are computed. For certain pulses we prove that the general rotation does not improve on the simpler rotation with fixed axis.
A general strategy to maintain the coherence of a quantum bit is proposed. The analytical result is derived rigorously including all memory and back-action effects. It is based on an optimized $π$-pulse sequence for dynamic decoupling extending the Carr-Purcell-Meiboom-Gill (CPMG) cycle. The optimized sequence is very efficient, in particular for strong couplings to the environment.
Reliable long-time storage of arbitrary quantum states is a key element for quantum information processing. In order to dynamically decouple a spin or quantum bit from a dephasing environment, we introduce an optimized sequence of $N$ control pulses of finite durations $τ\pp$ and finite amplitudes. The properties of this sequence of length $T$ stem from a mathematically rigorous derivation. Corrections occur only in order $T^{N+1}$ and $τ\pp^3$ without mixed terms such as $T^Nτ\pp$ or $T^Nτ\pp^2$. Based on existing experiments, a concrete setup for the verification of the properties of the adv…
The coherent control of small quantum system is considered. For a two-level system coupled to an arbitrary bath we consider a pulse of finite duration. We derive the leading and the next-leading order corrections to the evolution operator due to the non-commutation of the pulse and the bath Hamiltonian. The conditions are computed that make the leading corrections vanish. The pulse shapes optimized in this way are given for $π$ and $\fracπ{2}$ pulses.
Coherent control of two-state systems is traditionally achieved by resonant pulses of specific Rabi frequency and duration, by adiabatic techniques using level crossings or delayed pulses, or by sequences of pulses with precise relative phases (composite pulses). Here we develop a method for high-fidelity coherent control which uses a sequence of detuning pulses. By using the detuning pulse areas as control parameters, and driving on an analogy with composite pulses, we report a great variety of detuning pulse sequences for broadband and narrowband transition probability profiles.
We investigate the nature of the pulse sequence so that unwanted transitions in quantum systems can be inhibited optimally. For this purpose we show that the sequence of pulses proposed by Uhrig [Phys. Rev. Lett. \textbf{98}, 100504 (2007)] in the context of inhibition of environmental dephasing effects is optimal. We derive exact results for inhibiting the transitions and confirm the results numerically. We posit a very significant improvement by usage of the Uhrig sequence over an equidistant sequence in decoupling a quantum system from unwanted transitions. The physics of inhibition is the …
We present a time-dependent perturbative approach adapted to the treatment of intense pulsed interactions. We show there is a freedom in choosing secular terms and use it to optimize the accuracy of the approximation. We apply this formulation to a unitary superconvergent technique and improve the accuracy by several orders of magnitude with respect to the Magnus expansion.
We show that coherently driven atomic or molecular media potentially yield strong controllable short pulses of THz radiation. The method is based on excitation of maximal quantum coherence in a gas medium by optical pulses and coherent scattering of infra-red radiation to produce pulses of THz radiation. The pulses have the energies range from several nJ to $μ$J and time durations from several fs to ns at room temperature.
In the framework of nuclear magnetic resonance, we consider the general problem of the coherent control of a spin coupled to a bath by means of composite or continuous pulses of duration $τ_\mathrm{p}$. We show explicity that it is possible to design the pulse in order to achieve a decoupling of the spin from the bath up to the third order in $τ_\mathrm{p}$. The evolution of the system is separated in the evolution of the spin under the action of the pulse and of the bath times correction terms. We derive the correction terms for a general time dependent axis of rotation and for a general coup…
We prove the unconditional security of a quantum key distribution protocol in which bit values are encoded in the phase of a weak coherent-state pulse relative to a strong reference pulse. In contrast to implementations in which a weak pulse is used as a substitute for a single-photon source, the achievable key rate is found to decrease only linearly with the transmission of the channel.
Coherent pulse control for quantum memory is viable in the optical domain but nascent in microwave quantum circuits. We show how to realize coherent storage and on-demand pulse retrieval entirely within a superconducting circuit by exploiting and extending existing electromagnetically induced transparency technology in superconducting quantum circuits. Our scheme employs a linear array of superconducting artificial atoms coupled to a microwave transmission line.
The finite-amplitude short coherent control pulse with small random errors in its direction is considered. We derive the conditions for it to approximate an ideal delta-shaped pulse up to an error in the second order of pulse duration. Whether the symmetric and asymmetric pulse shapes would fulfill these conditions is also analyzed. The result shows that, under one of these conditions, all symmetric pulse shapes can fulfill this condition but not for all asymmetric ones..
We show how one can use the anisotropic properties of a coherent medium to separate temporally the two polarization components of a linearly polarized pulse. This is achieved by applying a control field such that one component of the pulse becomes ultraslow while the other component's group velocity is almost unaffected by the medium. We present analytical and numerical results to support the functioning of such a coherent medium as a polarization splitter of pulses.
We propose a scheme to engineer Schrödinger-cat states of propagating optical pulses. Multi-dimensional and multi-partite cat states can be generated simply by reflecting coherent optical pulses successively from a single-atom cavity. The influences of various sources of noise, including the atomic spontaneous emission and the pulse shape distortion, are characterized through detailed numerical simulation, which demonstrates practicality of this scheme within the reach of current experimental technology.
The total mass of noncollinear photons forming diverging light pulses is defined and found explicitly. Both classical and quantum derivations are presented. The quantum derivation is based on the use of multimode coherent states, and links between parameters of these states and those of the classical field strength are established.
We apply the techniques introduced in [Kraus et. al., Phys. Rev. Lett. 95, 080501, 2005] to prove security of quantum key distribution (QKD) schemes using two-way classical post-processing as well as QKD schemes based on weak coherent pulses instead of single-photon pulses. As a result, we obtain improved bounds on the secret-key rate of these schemes.
A general coherent control scenario to suppress, or accelerate, tunneling of quantum states decaying into a continuum, is investigated. The method is based on deterministic, or stochastic, sequences of unitary pulses that affect the underlying interference phenomena responsible for quantum dynamics, without inducing decoherence, or collapsing the coherent evolution of the system. The influence of control sequences on the ensuing quantum dynamics is analyzed by using perturbation theory to first order in the control pulse fields and compared to dynamical decoupling (DD) protocols and sequences …
We present experimental measurements on a model quantum system that demonstrate our ability to dramatically suppress qubit error rates by the application of optimized dynamical decoupling pulse sequences in a variety of experimentally relevant noise environments. We provide the first demonstration of an analytically derived pulse sequence developed by Uhrig, and find novel sequences through active, real-time experimental feedback. These new sequences are specially tailored to maximize error suppression without the need for a priori knowledge of the ambient noise environment. We compare these s…
Chiral molecules with broken parity symmetries can be modeled as quantum systems with cyclic-transition structures. By using these novel properties, we design two-step laser pulses to distinguish left- and right-handed molecules from the enantiomers. After the applied pulse drivings, one kind chiral molecules are trapped in coherent population trapping state, while the other ones are pumped to the highest states for ionizations. Then, different chiral molecules can be separated.
The resonator-induced phase gate is a multi-qubit controlled-phase gate for fixed-frequency superconducting qubits. Through off-resonant driving of a bus resonator, statically coupled qubits acquire a state-dependent phase. However, photon loss leads to dephasing during the gate, and any residual entanglement between the resonator and qubits after the gate leads to decoherence. Here we consider how to shape the drive pulse to minimize these unwanted effects. First, we review how the gate's entangling and dephasing rates depend on the system parameters and validate closed-form solutions against…
Optimized Slice-Phase Control of Mirror Pulse in Cold-Atom Interferometry with Finite Response Time
Huazhong University of Science and Technology（华中科技大学）；Wuhan Gravitation and Solid Earth Tides National Observation and Research Station（武汉重力与固体潮国家观测研究站）；Wuhan Institute of Quantum Technology（武汉量子技术研究院）
We investigate the problem of propagation of three-component resonant light pulses with adiabatically varying amplitudes through a medium consisting of atoms with the tripod level configuration. By means of both analytic and numerical methods we found the two modes of shape-preserving pulse propagation. The pulse propagation velocity is found to be either equal to the speed of light or significantly slowed down, depending on a particular propagation mode.
We propose technique of simultaneous excitation of disordered qubits providing an effective suppression of inhomogeneous broadening in their spectral density. The technique is based on applying of optimally chosen $π$-pulse with non-rectangular smooth shape. We study excitation dynamics of an off-resonant qubit subjected to strong classical electromagnetic driving field with the fast reference frequency and slow envelope. Within this solution we optimize the envelope to achieve a preassigned accuracy in qubit synchronization.
We study the conditions for two-photon classical interference with coherent pulses. We find that the temporal overlap between optical pulses is not required for interference However, coherence within the same inputs is found to be essential for the interference.
We analyze theoretically the impact of background counts on the efficiency of optical communication in the photon-starved regime using the pulse position modulation (PPM) format with direct detection. Degradation of the photon information efficiency is studied in the case when the background count rate is at most comparable with the rate of photodetection events generated by the incoming optical signal. The PPM symbol length is optimized under the constraint of a fixed average spectral power density using an analytical approximation. The results are compared with generalized on-off keying (OOK…
It is demonstrated that the properties of light stored in a four-level atomic system can be modified by an additional control interaction present during the storage stage. By choosing the pulse area of this interaction one can in particular continuously switch between two channels into which light is released.
We describe a technique for generating pulses of light with controllable photon numbers, propagation direction, timing, and pulse shapes. The technique is based on preparation of an atomic ensemble in a state with a desired number of atomic spin excitations, which is later converted into a photon pulse. Spatio-temporal control over the pulses is obtained by exploiting long-lived coherent memory for photon states and electromagnetically induced transparency (EIT) in an optically dense atomic medium. Using photon counting experiments we observe generation and shaping of few-photon sub-Poissonian…
The robustness of an atomic fountain interferometer with respect to variations in the initial velocity of the atoms and deviations from the optimal pulse amplitude is examined. We numerically simulate the dynamics of an interferometer in momentum space with a maximum separation of $20 \hbar k$ and map out the expected signal contrast depending on the variance of the initial velocity distribution and the value of the laser field amplitude. We show that an excitation scheme based on rapid adiabatic passage significantly enhances the expected signal contrast compared to the commonly used scheme c…
We present mirror and beamsplitter pulse designs that improve the fidelity of atom interferometry and increase its tolerance of systematic inhomogeneities. These designs are demonstrated experimentally with a cold thermal sample of $^{85}$Rb atoms. We first show a stimulated Raman inversion pulse design that achieves a ground hyperfine state transfer efficiency of 99.8(3)%, compared with a conventional $π$ pulse efficiency of 75(3)%. This inversion pulse is robust to variations in laser intensity and detuning, maintaining a transfer efficiency of 90% at detunings for which the $π$ pulse fideli…
We study beating of a probe field with a time-varying susceptibility in a coherently prepared Raman medium. We consider the general case of an arbitrary variation of susceptibility, which corresponds to a superposition of an arbitrary number of excited Raman transitions. We derive a general analytical solution and conservation relations for this process. We show that the interference between Raman polarizations may substantially affect frequency modulation and pulse compression for the probe field.
We investigate theoretically the phenomenon of so-called fast light in an unconventional regime, using pulses sufficiently short that relaxation effects in a gain medium can be ignored completely. We show that previously recognized gain instabilities, including superfluorescence, can be tolerated in achieving a pulse peak advance of one full peak width.
The aim of dynamical decoupling consists in the suppression of decoherence by appropriate coherent control of a quantum register. Effectively, the interaction with the environment is reduced. In particular, a sequence of $π$ pulses is considered. Here we present exact results on the suppression of the coupling of a quantum bit to its environment by optimized sequences of $π$ pulses. The effect of various cutoffs of the spectral density of the environment is investigated. As a result we show that the harder the cutoff is the better an optimized pulse sequence can deal with it. For cutoffs which…
We present a detailed analysis of the recently demonstrated technique to generate quasi-stationary pulses of light [M. Bajcsy {\it et al.}, Nature (London) \textbf{426}, 638 (2003)] based on electromagnetically induced transparency. We show that the use of counter-propagating control fields to retrieve a light pulse, previously stored in a collective atomic Raman excitation, leads to quasi-stationary light field that undergoes a slow diffusive spread. The underlying physics of this process is identified as pulse matching of probe and control fields. We then show that spatially modulated contro…
Qubits driven by resonant strong pulses are studied and a parameter regime is explored in which the dynamics can be solved in closed form. Instantaneous coherent destruction of tunneling can be seen for longer pulses, whereas shorter pulses allow a fast preparation of the qubit state. Results are compared with recent experiments of pulsed nitrogen-vacancy center spin qubits in diamond.
Photon echo schemes are excellent candidates for high efficiency coherent optical memory. They are capable of high-bandwidth multi-pulse storage, pulse resequencing and have been shown theoretically to be compatible with quantum information applications. One particular photon echo scheme is the gradient echo memory (GEM). In this system, an atomic frequency gradient is induced in the direction of light propagation leading to a Fourier decomposition of the optical spectrum along the length of the storage medium. This Fourier encoding allows precision spectral manipulation of the stored light. I…
Spin squeezed states are a class of entangled states of spins that have practical applications to precision measurements. In recent years spin squeezing with one-axis twisting (OAT) has been demonstrated experimentally with spinor BECs with more than 10^3 atoms. Although the noise is below the standard quantum limit, the OAT scheme cannot reduce the noise down to the ultimate Heisenberg limit. Here we propose an experimentally feasible scheme based on optimized quantum control to greatly enhance the performance of OAT to approach the Heisenberg limit, requiring only an OAT Hamiltonian and the …
A pulse shaping algorithm for a matter wave with the purpose of controlling a binary reaction has been designed. The scheme is illustrated for an Eley-Rideal reaction where an impinging matter-wave atom recombines with an adsorbed atom on a metal surface. The wave function of the impinging atom is shaped such that the desorbing molecule leaves the surface in a specific vibrational state.
We demonstrate experimentally a quantum memory scheme for the storage of weak coherent light pulses in an inhomogeneously broadened optical transition in a Pr^{3+}: YSO crystal at 2.1 K. Precise optical pumping using a frequency stable (about 1kHz linewidth) laser is employed to create a highly controllable Atomic Frequency Comb (AFC) structure. We report single photon storage and retrieval efficiencies of 25%, based on coherent photon echo type re-emission in the forward direction. The coherence property of the quantum memory is proved through interference between a super Gaussian pulse and t…
We show that a single, trapped, laser-driven atom in a high-finesse optical cavity allows for the quantum-coherent generation of entangled light pulses on demand. Schemes for generating simultaneous and temporally separated pulse pairs are proposed. The mechanical effect of the laser excitation on the quantum motion of the cold trapped atom mediates the entangling interaction between two cavity modes and between the two subsequent pulses, respectively. The entanglement is of EPR-type, and its degree can be controlled through external parameters. At the end of the generation process the atom is…
We present exact analytic formulae which describe the interaction of multistate quantum systems possessing the Majorana and Morris-Shore dynamic symmetries with a train of pulses. The pulse train field can be viewed as repeated interactions of the quantum system with the same field and hence the overall propagator is expressed as the matrix power of the single-pulse propagator. Because of the Majorana and Morris-Shore symmetries the multistate dynamics is characterised by intrinsic two-state features, described by one or more pairs of complex-valued Cayley-Klein parameters. This facilitates th…
The response of an arbitrary closed quantum system to a partially coherent electric field is investigated, with a focus on the transient coherences in the system. As a model we examine, both perturbatively and numerically, the coherences induced in a three level $V$ system. Both rapid turn-on and pulsed turn-on effects are investigated. The effect of a long and incoherent pulse is also considered, demonstrating that during the pulse the system shows a coherent response which reduces after the pulse is over. Both the pulsed scenario and the thermally broadened CW case approach a mixed state in …
We have shown that a coherently driven solid state medium can potentially produce strong controllable short pulses of THz radiation. The high efficiency of the technique is based on excitation of maximal THz coherence by applying resonant optical pulses to the medium. The excited coherence in the medium is connected to macroscopic polarization coupled to THz radiation. We have performed detailed simulations by solving the coupled density matrix and Maxwell equations. By using a simple $V$-type energy scheme for ruby, we have demonstrated that the energy of generated THz pulses ranges from hund…
We study multiple-spin coherence transfers in linear Ising spin chains with nearest neighbor couplings. These constitute a model for efficient information transfers in future quantum computing devices and for many multi-dimensional experiments for the assignment of complex spectra in nuclear magnetic resonance spectroscopy. We complement prior analytic techniques for multiple-spin coherence transfers with a systematic numerical study where we obtain strong evidence that a certain analytically-motivated family of restricted controls is sufficient for time-optimality. In the case of a linear thr…
Unconditional security proofs of the Bennett-Brassard protocol of quantum key distribution have been obtained recently. These proofs cover also practical implementations that utilize weak coherent pulses in the four signal polarizations. Proven secure rates leave open the possibility that new proofs or new public discussion protocols obtain larger rates over increased distance. In this paper we investigate limits to error rate and signal losses that can be tolerated by future protocols and proofs.
Coherent control of traveling acoustic excitations in a waveguide system is an interesting way to manipulate and transduce classical and quantum information. So far, these interactions, often based on optomechanical resonators or Brillouin scattering, have been studied in the steady-state regime using continuous waves. However, waveguide experiments are often based on optical pump pulses which require treatment in a dynamic framework. In this paper, we present an effective Hamiltonian formalism in the dynamic regime using optical pulses that links waveguide optomechanics and cavity optomechani…
We investigate the effectiveness of different dynamical decoupling protocols for storage of a single qubit in the presence of a purely dephasing bosonic bath, with emphasis on comparing quantum coherence preservation under uniform vs. non-uniform delay times between pulses. In the limit of instantaneous bit-flip pulses, this is accomplished by establishing a new representation of the controlled qubit evolution, where the resulting decoherence behaviour is directly expressed in terms of the free evolution. Simple analytical expressions are given to approximate the long- and short- term coherenc…
Bell state analyzer (BSA) is one of the most crucial apparatus in photonic quantum information processing. While linear optics provide a practical way to implement BSA, it provides unavoidable errors when inputs are not ideal single-photon states. Here, we propose a simple method to deduce the BSA for single-photon inputs using weak coherent pulses. By applying the method to Reference-Frame-Independent Measurement-Device-Independent Quantum Key Distribution, we experimentally verify the feasibility and effectiveness of the method.
In this work, we consider a two-level system (TLS) coupled to a one-dimensional continuum of bosonic modes in a transmission line. Using the master equation approach, a method for determining the photon number distribution of the scattered field is outlined. Specifically, results for the reflected field when driving the TLS with a coherent pulse are given. While the one-photon probability is enhanced compared to the incident coherent field, the system is still not a good deterministic single-photon source. Extending the system to contain two separate transmission lines, however, output fields …
Experimental realizations of two qubit entangling gates with trapped ions typically rely on addressing spectroscopically resolved motional sidebands, limiting gate speed to the secular frequency. Fast entangling gates using ultrafast pulsed lasers overcome this speed limit. This approach is based on state-dependent photon recoil kicks from a sequence of counter-propagating, resonant, ultrafast pulse pairs, which can allow sub-microsecond gate speeds. Here we demonstrate a key component of the ultrafast gate protocol, the coherent excitation of a 171Yb+ ion across the 2S1/2-2P1/2 transition wit…
We demonstrate the generation of coherent Stokes pulses with randomized linear-polarization in diamond, when the pump wave-vector and linear polarization were oriented along the $[110]$ and $[1\bar{1}0]$ axes respectively. In this configuration the excitation of multiple Raman modes produces isotropic gain, preventing the Stokes pulse from acquiring a deterministic orientation and is instead randomized by the zero-point motion of the crystal. Experimental polarization measurements were consistent with an independent, identical distribution with an estimated entropy rate of 6.67 bits per pulse.
We analyze the effects of partial coherence of ground state preparation on two-pulse propagation in a three-level $Λ$ medium, in contrast to previous treastments that have considered the cases of media whose ground states are characterized by probabilities (level populations) or by probability amplitudes (coherent pure states). We present analytic solutions of the Maxwell-Bloch equations, and we extend our analysis with numerical solutions to the same equations. We interpret these solutions in the bright/dark dressed state basis, and show that they describe a population transfer between the br…
We show that the physical mechanism of population transfer in a 3-level system with a closed loop of coherent couplings (loop-STIRAP) is not equivalent to an adiabatic rotation of the dark-state of the Hamiltonian but coresponds to a rotation of a higher-order trapping state in a generalized adiabatic basis. The concept of generalized adiabatic basis sets is used as a constructive tool to design pulse sequences for stimulated Raman adiabatic passage (STIRAP) which give maximum population transfer also under conditions when the usual condition of adiabaticty is only poorly fulfilled. Under cert…
The proposal for quantum computing with rare-earth-ion qubits in inorganic crystals makes use of the inhomogeneous broadening of optical transitions in the ions to associate individual qubits with ions responding to radiation in selected frequency channels. We show that a class of Gaussian composite pulses and complex sech pulses provide accurate qubit pi-rotations, which are at the same time channel selective on a 5 MHz frequency scale and tolerant to 0.5 MHz deviations of the transition frequency of ions within a single channel. Rotations in qubit space of arbitrary angles and phases are pro…
We utilize genetic algorithms to find optimal dynamical decoupling (DD) sequences for a single-qubit system subjected to a general decoherence model under a variety of control pulse conditions. We focus on the case of sequences with equal pulse-intervals and perform the optimization with respect to pulse type and order. In this manner we obtain robust DD sequences, first in the limit of ideal pulses, then when including pulse imperfections such as finite pulse duration and qubit rotation (flip-angle) errors. Although our optimization is numerical, we identify a deterministic structure underlie…
The performance of sequences of designed pulses of finite length $τ$ is analyzed for a bath of spins and it is compared with that of sequences of ideal, instantaneous pulses. The degree of the design of the pulse strongly affects the performance of the sequences. Non-equidistant, adapted sequences of pulses, which equal instantaneous ones up to $\mathcal{O}(τ^3)$, outperform equidistant or concatenated sequences. Moreover, they do so at low energy cost which grows only logarithmically with the number of pulses, in contrast to standard pulses with linear growth.
We present a scalable scheme to design optimized soft pulses and pulse sequences for coherent control of interacting quantum many-body systems. The scheme is based on the cluster expansion and the time dependent perturbation theory implemented numerically. This approach offers a dramatic advantage in numerical efficiency, and it is also more convenient than the commonly used Magnus expansion, especially when dealing with higher order terms. We illustrate the scheme by designing 2nd-order pi-pulses and a 6th-order 8-pulse refocusing sequence for a chain of qubits with nearest-neighbor couplings…
