We propose an experimentally accessible procedure for conditional preparation of highly non-classical states of collective spin of an atomic ensemble. The quantum state engineering is based on a combination of QND interaction between atoms and light previously prepared in a non-Gaussian state using photon subtraction from squeezed vacuum beam, homodyne detection on the output light beam, and a coherent displacement of atomic state. The procedure is capable of non-deterministic preparation of a wide class of superpositions of atomic Dicke states. We present several techniques to optimize the performance of the protocol and maximize the trade-off between fidelity of prepared state and success probability of the scheme.
A scheme for preparing Schrödinger cat (SC) states is proposed beyond the Lamb-Dicke limit in a Raman-$Λ$-type configuration. It is shown that SC states can be obtained more efficiently with our scheme than with the former ones.
We characterize the long-time projective behavior of the stochastic master equation describing a continuous, collective spin measurement of an atomic ensemble both analytically and numerically. By adding state based feedback, we show that it is possible to prepare highly entangled Dicke states deterministically.
We investigate the dynamics of a cold trapped ion coupled to the quantized field inside a high-finesse cavity. We have used an approach for preparing the SC states of motion of ion. This approach, based on unitary transformating the Hamiltonian, allows its exact diagonalization without performing the Lamb-Dicke aproximation. We show that is possible to generate a SC states having rather simple initial state preparation, e.g., the vacuum sate for both cavity field and the ion motion.
A method is presented to transfer a system of two-level atoms from a spin coherent state to a maximally spin squeezed Dicke state, relevant for quantum metrology and quantum information processing. The initial state is the ground state of an initial linear Hamiltonian which is gradually turned into a final quadratic Hamiltonian whose ground state is the selected Dicke state. We use compensating operators to suppress diabatic transitions to unwanted states that would occur if the change were not slow. We discuss the possibilities of constructing the compensating operators by sequential applicat…
The exact number of CNOT and single qubit gates needed to implement a Quantum Algorithm in a given architecture is one of the central problems of Quantum Computation. In this work we study the importance of concise realizations of Partially defined Unitary Transformations for better circuit construction using the case study of Dicke State Preparation. The Dicke States $(\left|D^n_k \right>)$ are an important class of entangled states with uses in many branches of Quantum Information. In this regard we provide the most efficient Deterministic Dicke State Preparation Circuit in terms of CNOT and…
Deterministic preparation of entangled Dicke states
Institute for Quantum Science and Engineering, Texas A&M University（德州农工大学量子科学与工程研究所）；Department of Biological and Agricultural Engineering, Texas A&M University（德州农工大学生物与农业工程系）
We propose a simple technique for the generation of arbitrary-sized Dicke states in a chain of trapped ions. The method uses global addressing of the entire chain by two pairs of delayed but partially overlapping laser pulses to engineer a collective adiabatic passage along a multi-ion dark state. Our technique, which is a many-particle generalization of stimulated Raman adiabatic passage (STIRAP), is decoherence-free with respect to spontaneous emission and robust against moderate fluctuations in the experimental parameters. Furthermore, because the process is very rapid, the effects of heati…
We investigate the quantum non-demolition (QND) measurement of an atomic population based on a heterodyne detection and show that the induced back-action allows to prepare both spin-squeezed and Dicke states. We use a wavevector formalism to describe the stochastic process of the measurement and the associated atomic evolution. Analytical formulas of the atomic distribution momenta are derived in the weak coupling regime both for short and long time behavior, and they are in good agreement with those obtained by a Monte-Carlo simulation. The experimental implementation of the proposed heterody…
We have investigated theoretically and experimentally a method for preparing Dicke states in trapped atomic ions. We consider a linear chain of $N$ ion qubits that is prepared in a particular Fock state of motion, $|m>$. The $m$ phonons are removed by applying a laser pulse globally to the $N$ qubits, and converting the motional excitation to $m$ flipped spins. The global nature of this pulse ensures that the $m$ flipped spins are shared by all the target ions in a state that is a close approximation to the Dicke state $\D{N}{m}$. We calculate numerically the fidelity limits of the protocol an…
Data and code for collision-model Dicke-state preparation: depth-fidelity frontiers, circuit costs, and superconducting-processor measurements
Saint Louis University（圣路易斯大学）；KT One；University of South Florida（南佛罗里达大学）；Koç University（科奇大学）；TÜBİTAK Research Institute for Fundamental Sciences (TBAE)（土耳其科技研究基金会基础科学研究所（TBAE））；Tokyo International University（东京国际大学）；Nanoelectronics Research Center（纳米电子学研究中心）
The Dicke state $|D_k^n\rangle$ is an equal-weight superposition of all $n$-qubit states with Hamming Weight $k$ (i.e. all strings of length $n$ with exactly $k$ ones over a binary alphabet). Dicke states are an important class of entangled quantum states that among other things serve as starting states for combinatorial optimization quantum algorithms. We present a deterministic quantum algorithm for the preparation of Dicke states. Implemented as a quantum circuit, our scheme uses $O(kn)$ gates, has depth $O(n)$ and needs no ancilla qubits. The inductive nature of our approach allows for lin…
For donor nuclear spins in silicon, we show how to deterministically prepare various symmetric and asymmetric Dicke states which span a complete basis of the many-body Hilbert space. The state preparation is realized by cooperative pumping of nuclear spins by coupled donor electrons, and the required controls are in situ to the prototype Kane proposal for quantum computation. This scheme only requires a sub-gigahertz donor exchange coupling which can be readily achieved without atomically precise donor placement, hence it offers a practical way to prepare multipartite entanglement of spins in …
We present a Dicke state preparation scheme which uses global control of $N$ spin qubits: our scheme is based on the standard phase estimation algorithm, which estimates the eigenvalue of a unitary operator. The scheme prepares a Dicke state non-deterministically by collectively coupling the spins to an ancilla qubit via a $ZZ$-interaction, using $\ceil*{\log_2 N} + 1$ ancilla qubit measurements. The preparation of such Dicke states can be useful if the spins in the ensemble are used for magnetic sensing: we discuss a possible realization using an ensemble of electronic spins located at diamon…
We propose a method to deterministically prepare a desired quantum state in a one-dimensional (1D) continuum by a shaped photon pulse. This method is based on time-reverse of the quantum emission process. We show that the desired quantum state such as Dicke or timed-Dicke state can be successfully prepared with very high fidelity even if the dissipation to the environment is nonnegligible and the pulse shaping is not perfect. We also show that large quantum entanglement between emitters can be created by just a single photon pulse. This method is experimentally feasible in 1D waveguide-QED or …
We present a divide-and-conquer approach to deterministically prepare Dicke states $\lvert D_k^n\rangle$ (i.e., equal-weight superpositions of all $n$-qubit states with Hamming Weight $k$) on quantum computers. In an experimental evaluation for up to $n=6$ qubits on IBM Quantum Sydney and Montreal devices, we achieve significantly higher state fidelity compared to previous results [Mukherjee and others, TQE'2020], [Cruz and others, QuTe'2019]. The fidelity gains are achieved through several techniques: Our circuits first "divide" the Hamming weight between blocks of $n/2$ qubits, and then "con…
There has been an extensive development in the use of multi-partite entanglement as a resource for various quantum information processing tasks. In this paper we focus on preparing arbitrary spin eigenstates whose subset contain important entangled resources like Dicke states as well as some other sub-radiant states that are difficult to prepare. Leveraging on the symmetry of these states we consider uniform pairwise exchange coupling between every pair of qubits. Starting from a product state of a given spin eigenstate with a single qubit state, another spin eigenstate can be prepared using s…
A scheme, where three atomic ensembles can be prepared in the states of the W-class via Raman type interaction of strong classical field and a projection measurement involved three single-photon detectors and two beamsplitters, are considered. The obtained atomic entanglement consists of the Dicke or W-states of each of the ensembles.
We study the conditional preparation of single photons based on parametric downconversion, where the detection of one photon from a given pair heralds the existence of a single photon in the conjugate mode. We derive conditions on the modal characteristics of the photon pairs, which ensure that the conditionally prepared single photons are quantum-mechanically pure. We propose specific experimental techniques that yield photon pairs ideally suited for single-photon conditional preparation.
The quantum spin states of atomic ensemble are of special interesting for both fundamental studies and precision measurement applications. Here, we propose a scheme to prepare collective quantum states of an atomic ensemble placed in an optical cavity via homodyne measurement of probing light field. The effective interactions of atoms mediated by photons are enhanced by the optical cavity, and the output probe light could also be entangled with the collective spin states. By selectively measuring the quadrature of output light, we can prepare various quantum states, including superposition sta…
Based on the exact conditional quantum dynamics for a two-ion system, we propose an efficient {\it single-step} scheme for coherently manipulating quantum information of two trapped cold ions by using a pair of synchronous laser pulses. Neither the auxiliary atomic level nor the Lamb-Dicke approximation are needed.
A simple experimental setup consisting of a spontaneous parametric down-conversion source and passive linear optics is proposed for conditional preparation of a maximally entangled polarization state of two photons. Successful preparation is unambiguously heralded by coincident detection of four auxiliary photons. The proposed scheme utilizes the down-conversion term corresponding to the generation of three pairs of photons. We analyze imperfect detection of the auxiliary photons and demonstrate that its deleterious effect on the fidelity of the prepared state can be suppressed at the cost of …
We study the characteristics of the quantum state of light produced by a conditional preparation protocol totally performed in the continuous variable regime. It relies on conditional measurements on quantum intensity correlated bright twin beams emitted by a non-degenerate OPO above threshold. Analytical expressions as well as computer simulations of the selected state properties and preparation efficiency are developed and show that a sub-Poissonian state can be produced by this technique. Projection onto a given trigger value is studied and then extended to a finite band. The continuous var…
A fundamental prerequisite for the implementation of linear optical quantum computation is a source of single-photon wavepackets capable of high-visibility interference in scalable networks. These conditions can be met with micro-structured waveguides in conjunction with ultra-short classical timing pulses. By exploiting a novel type-II phasematching configuration we demonstrate a waveguided single photon source exhibiting a conditional detection efficiency exceeding 51% (which corresponds to a preparation efficiency of 85%) and extraordinarily high detection rates of up to 8.5x10^5 coincidenc…
We discuss the conditional preparation of single photons via parametric down-conversion. This technique is commonly used as a single photon source in modern quantum optics experiments. A significant problem facing this technique is the inability of present day photo-detectors to resolve photon number. This results in mixing with higher photon number terms. To overcome this several techniques have been proposed, including multi-port detection and time-division multiplexing. These techniques help approximate number resolving detection even when using non-number resolving detectors. In this paper…
We report the first experimental demonstration of conditional preparation of a non classical state of light in the continuous variable regime. Starting from a non degenerate OPO which generates above threshold quantum intensity correlated signal and idler "twin beams", we keep the recorded values of the signal intensity only when the idler falls inside a band of values narrower than its standard deviation. By this very simple technique, we generate a sub-Poissonian state 4.4dB below shot noise from twin beams exhibiting 7.5dB of noise reduction in the intensity difference.
Non-Gaussian states of an optical field are important as a proposed resource in quantum information applications. While conditional preparation is a highly successful approach to preparing such states, their quality is limited by detector non-idealities such as dead time, narrow dynamic range, limited quantum efficiency and dark noise. Mesoscopic photon counters, with peak performance at higher photon number, offer many practical advantages over single-photon level conditioning detectors. Here we propose a novel approach involving displacement of the ancilla field into the regime where mesosco…
A technique for conditionally creating single- or multimode photon-number states is analyzed using Bayesian theory. We consider the heralded N-photon states created from the photons produced by an unseeded optical parametric amplifier when the heralding detector is the time-multiplexed photon-number-resolving detector recently demonstrated by Fitch, et al. [Phys. Rev. A 68, 043814 (2003).] and simultaneously by Achilles, et al. [Opt. Lett. 28, 2387 (2003).]. We find that even with significant loss in the heralding detector, fields with sub-Poissonian photon-number distributions can be created.…
We propose a scheme for producing large Fock states in Cavity QED via the implementation of a highly selective atom-field interaction. It is based on Raman excitation of a three-level atom by a classical field and a quantized field mode. Selectivity appears when one tunes to resonance a specific transition inside a chosen atom-field subspace, while other transitions remain dispersive, as a consequence of the field dependent electronic energy shifts. We show that this scheme can be also employed for reconstructing, in a new and efficient way, the Wigner function of the cavity field state.
Based on the conditional quantum dynamics of laser-ion interaction, we propose an efficient theoretical scheme to deterministically generate quantum pure states of a single trapped cold ion without performing the Lamb-Dicke approximation. An arbitrary quantum state can be created by using a series of classical laser beams with selected frequencies, initial phases and durations. As special examples, we further show how to create or approximate several typical macroscopic quantum states, such as the phase state and (even/odd) coherent states. Unlike previous schemes operated in the Lamb-Dicke re…
We show that conditional output measurement on a beam splitter may be used to produce photon-added states for a large class of signal-mode quantum states, such as thermal states, coherent states, squeezed states, displaced photon-number states, and coherent phase states. Combining a mode prepared in such a state and a mode prepared in a photon-number state, the state of the mode in one of the output channels of the beam splitter ``collapses'' to a photon-added state, provided that no photons are detected in the other output channel. We present analytical and numerical results, with special emp…
An energy gap develops near quantum critical point of quantum phase transition in a finite many-body (MB) system, facilitating the ground state transformation by adiabatic parameter change. In real application scenarios, however, the efficacy for such a protocol is compromised by the need to balance finite system life time with adiabaticity, as exemplified in a recent experiment that prepares three-mode balanced Dicke state near deterministically [PNAS {\bf 115}, 6381 (2018)]. Instead of tracking the instantaneous ground state as unanimously required for most adiabatic crossing, this work repo…
In an experiment reported recently [Phys. Rev. Lett. 100, 133601 (2008)], we demonstrated that, through group velocity matched parametric downconversion, heralded single photons can be generated in pure quantum states without spectral filtering. The technique relies on factorable photon pair production, initially developed theoretically in the strict collinear regime; focusing - required in any experimental implementation - can ruin this factorability. Here we present the numerical model used to design our single photon sources and minimize spectral correlations in the light of such experiment…
The U(1,1) and U(2) transformations realized by three-mode interaction in the respective parametric approximations are studied in conditional measurement, and the corresponding non-unitary transformation operators are derived. As an application, the preparation of single-mode quantum states using an optical feedback loop is discussed, with special emphasis of Fock state preparation. For that example, the influence of non-perfect detection and feedback is also considered.
Continuous variable remote state preparation and teleportation are analyzed using Wigner functions in phase space. We suggest a remote squeezed state preparation scheme between two parties sharing an entangled twin beam, where homodyne detection on one beam is used as a conditional source of squeezing for the other beam. The scheme works also with noisy measurements, and provide squeezing if the homodyne quantum efficiency is larger than 50%. Phase space approach is shown to provide a convenient framework to describe teleportation as a generalized conditional measurement, and to evaluate relev…
We apply wave packet methods to study an ion-trap system in the strong excitation regime imposing neither the rotating wave nor the Lamb-Dicke approximations. By this approach we show the existence of states with restricted phase space evolution, as a genuine consequence of quantum interference between wave packet fractions. A particular instance of such a state oscillates between maximal entanglement and pure disentanglement between the constitute subsystems. The characteristic crossover time is very rapid making them suitable for state preparations of EPR or Schrodinger cat states. Over long…
We propose a robust scheme for generating macroscopic superposition states of spin or motion with the aid of a single photon. Shaping the wave packet of the photon enables high-fidelity preparation of non-classical states of matter even in the presence of photon loss. Success is heralded by photodetection, enabling the scheme to be implemented with a weak coherent field. We analyze applications to preparing Schrödinger cat states of a collective atomic spin or of a mechanical oscillator coupled to an optical resonator. The method generalizes to preparing arbitrary superpositions of coherent st…
We develop a general formalism, based on the Wigner function representation of continuous-variable quantum states, to describe the action of an arbitrary conditional operation on a multimode Gaussian state. We apply this formalism to several examples, thus showing its potential as an elegant analytical tool for simulating quantum optics experiments. Furthermore, we also use it to prove that EPR steering is a necessary requirement to remotely prepare a Wigner-negative state.
State preparation via conditional output measurement on a beam splitter is studied, assuming the signal mode is mixed with a mode prepared in a Fock state and photon numbers are measured in one of the output channels. It is shown that the mode in the other output channel is prepared in either a photon-subtracted or a photon-added Jacobi polynomial state, depending upon the difference between the number of photons in the input Fock state and the number of photons in the output Fock state onto which it is projected. The properties of the conditional output states are studied for coherent and squ…
