I. K. Kominis
The suppression of spin-exchange relaxation in dense alkali-metal vapors discovered in 1973 and governing modern atomic magnetometers is here reformulated in terms of quantum measurement theory and the quantum Zeno effect. This provides a new perspective of understanding decoherence in spin-polarized atomic vapors.
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We analyse non-quadratic in time Zeno effect which arises when a few-atom state initially trapped between two high laser-induced barriers is briefly released to free evolution. We identify the Zeno time, analyse the energy distributions of those atoms which have escaped an remained inside the trap, and obtain a simple relation between the survival and non-escape probabilities. The relevant time scales are such that the effect would be observable for the atomic species used in current laser experiments.
We propose an interesting scheme for distributed orbital state quantum cloning with atomic ensembles based on the quantum Zeno dynamics. These atomic ensembles which consist of identical three-level atoms are trapped in distant cavities connected by a single-mode integrated optical star coupler. These qubits can be manipulated through appropriate modulation of the coupling constants between atomic ensemble and classical field, and the cavity decay can be largely suppressed as the number of atoms in the ensemble qubits increases. The fidelity of each cloned qubit can be obtained with analytic r…
In this paper, we first demonstrate how to realize quantum state transferring (QST) from one atom to another based on quantum Zeno dynamics. Then, the QST protocol is generalized to realize the quantum state swapping (QSS) between two arbitrary atoms with the help of a third one. Furthermore, we also consider the QSS within a quantum network. The influence of decoherence is analyzed by numerical calculation. The results demonstrate that the protocols are robust against cavity decay.
Quantum entanglement is important quanum resources in quantum information sicence. Here we propose an approach to {preparing} atomic quantum entanglement in a hybrid atom-cavity-fiber system. Using quantum Zeno dynamics method, the system evolution states are always split into a series of Zeno invariant {subspaces} consisting of dark and bright states. By choosing the initial state of the system, the bright states are all neglected and only dark states are kept to build the effective Hamiltonian. By tuning the system parameters, two-atom multiple-dimensional entanglement, two-atom Bell state, …
We propose a scheme for preparation of large-scale entangled $W$ states based on the fusion mechanism via quantum Zeno dynamics. By sending two atoms belonging to an $n$-atom $W$ state and an $m$-atom $W$ state, respectively, into a vacuum cavity (or two separate cavities), we may obtain a ($n+m-2$)-atom $W$ state via detecting the two-atom state after interaction. The present scheme is robust against both spontaneous emission of atoms and decay of cavity, and the feasibility analysis indicates that it can also be realized in experiment.
The effect of the anti-rotating terms on the short-time evolution and the quantum Zeno (QZE) and anti-Zeno (AQZE) effects is studied for a two-level system coupled to a bosonic environment. A unitary transformation and perturbation theory are used to obtain the electron self-energy, energy shift and the enhanced QZE or the AQZE, simultaneously. The calculated Zeno time depends on the atomic transition frequency sensitively. When the atomic transition frequency is smaller than the central frequency of the spectrum of boson environment, the Zeno time is prolonged and the anti-rotating terms enha…
The so-called quantum Zeno effect is essentially a consequence of the projection postulate for ideal measurements. To test the effect Itano et al. have performed an experiment on an ensemble of atoms where rapidly repeated level measurements were realized by means of short laser pulses. Using dynamical considerations we give an explanation why the projection postulate can be applied in good approximation to such measurements. Corrections to ideal measurements are determined explicitly. This is used to discuss in how far the experiment of Itano et al. can be considered as a test of the quantum …
Frequent measurements can modify the decay of an unstable quantum state with respect to the free dynamics given by Fermi's golden rule. In a landmark article, Nature 405, 546 (2000), Kofman and Kurizki concluded that in quantum decay processes, acceleration of the decay by frequent measurements, called the quantum anti-Zeno effect (AZE), appears to be ubiquitous, while its counterpart, the quantum Zeno effect, is unattainable. However, up to now there have been no experimental observations of the AZE for atomic radiative decay (spontaneous emission) in free space. In this work, making use of a…
It is shown that inverse quantum Zeno effect (IZE) may exist in a three-level system with Rabi oscillations between discrete atomic states. The experiment to observe IZE in such a system is proposed.
We show that nonlinear interactions induce both the Zeno and anti-Zeno effects in the generalised Bose-Josephson model (with the on-site interactions and the second-order tunneling) describing Bose-Einstein condensate in double-well trap subject to particle removal from one of the wells. We find that the on-site interactions induce \textit{only} the Zeno effect, which appears at long evolution times, whereas the second-order tunneling leads to a strong decay of the atomic population at short evolution times, reminiscent of the anti-Zeno effect, and destroys the nonlinear Zeno effect due to the…
Magnetic-sensitive radical-ion-pair reactions are understood to underlie the biochemical magnetic compass used by avian species for navigation. Recent experiments have provided growing evidence for the radical-ion-pair magnetoreception mechanism, while recent theoretical advances have unravelled the quantum nature of radical-ion-pair reactions, which were shown to manifest a host of quantum-information-science concepts and effects, like quantum measurement, quantum jumps and the quantum Zeno effect. We here show that the quantum Zeno effect provides for the robustness of the avian compass mech…
We study one-step implementation of the Fredkin gate in a bi-modal cavity under both resonant and large detuning conditions based on quantum Zeno dynamics, which reduces the complexity of experiment operations. The influence of cavity decay and atomic spontaneous emission is discussed by numerical calculation. The results demonstrate that the fidelity and the success probability are robust against cavity decay in both models and they are also insensitive to atomic spontaneous emission in the large detuning model. In addition, the interaction time is rather short in the resonant model compared …
The accuracy of an atomic clock depends in part on the bandwidth of the relevant atomic transitions. Here we consider an ensemble of $N$ atoms whose transition frequencies have been independently perturbed by environmental effects or other factors. We consider the possibility of using the quantum Zeno effect to lock the relative phase of the atoms, which would decrease their effective bandwidth by a factor of $1/\sqrt{N}$. We analyze an example in which the quantum Zeno effect can be used to lock the relative phase of a pair of atoms, after which the elapsed time can be determined. Practical a…
The projection postulate has been used to predict a slow-down of the time evolution of the state of a system under rapidly repeated measurements, and ultimately a freezing of the state. To test this so-called quantum Zeno effect an experiment was performed by Itano et al. (Phys. Rev. A 41, 2295 (1990)) in which an atomic-level measurement was realized by means of a short laser pulse. The relevance of the results has given rise to controversies in the literature. In particular the projection postulate and its applicability in this experiment have been cast into doubt. In this paper we show anal…
In a quantum world, a watched arrow never moves. This is the Quantum Zeno Effect (QZE). Repeatedly asking a quantum system "are you still in your initial state?" blocks its coherent evolution through measurement back-action. Quantum Zeno Dynamics (QZD) leaves more freedom to the system. Instead of pinning it to a single state, it sets a border in its evolution space. Repeatedly asking the system "did you cross the border?" makes it impenetrable. Since the border can be designed at will by choosing the measured observable, QZD allows one to tailor the system's evolution space. Recent proposals,…
We discuss a proposal for the efficient generation of the maximally entangled atomic N-GHZ state in a spinor-1 condensate by driving internal state atomic Raman transitions using (classical) laser fields. We illustrate the dynamics in terms of a quantum Zeno subspace, and identify the resultant atomic elastic collision in facilitating the deterministic entanglement creation. Our proposal can be readily implemented in several laboratories where ferromagnetic spinor condensates (of $^{87}$Rb atoms) are investigated.
Latent Symmetry in Quantum Zeno Dynamics
该研究揭示量子芝诺动力学中存在潜在对称性，以电路量子电动力学网络为对象，发现其可在几何不等价的测量选定子空间间建立精确关系，是量子芝诺动力学的隐藏组织原则。
We propose a selfconsistent quantum mechanical approach to study the dynamics of a two-level system subject to random time evolution. This randomness gives rise to competing effects between dissipative and non-dissipative decoherence with a consequent slow down of the atomic decay rate.
We show that atomic spin motion can be controlled by circularly polarized light without light absorption in the strong pumping limit. In this limit, the pumping light, which drives the empty spin state, destroys the Zeeman coherence effectively and freezes the coherent transition via the quantum Zeno effect. It is verified experimentally that the amount of light absorption decreases asymptotically to zero as the incident light intensity is increased.
We propose a new methodology, namely "quantum Zeno blockade," for managing light scattering at a few-photon level in general nonlinear-optical media, such as crystals, fibers, silicon microrings, and atomic vapors. Using this tool, antibunched emission of photon pairs can be achieved, leading to potent quantum-optics applications such as deterministic entanglement generation without the need for heralding. In a practical implementation using an on-chip toroidal microcavity immersed in rubidium vapor, we estimate that high-fidelity entangled photons can be produced on-demand at MHz rates or hig…
The protection of the coherence of open quantum systems against the influence of their environment is a very topical issue. A scheme is proposed here which protects a general quantum system from the action of a set of arbitrary uncontrolled unitary evolutions. This method draws its inspiration from ideas of standard error-correction (ancilla adding, coding and decoding) and the Quantum Zeno Effect. A pedagogical demonstration of our method on a simple atomic system, namely a Rubidium isotope, is proposed.
The driven evolution of the spin of an individual atomic ion on the ground-state hyperfine resonance is impeded by the observation of the ion in one of the pertaining eigenstates. Detection of resonantly scattered light identifies the ion in its upper ``bright'' state. The lower ``dark'' ion state is free of relaxation and correlated with the detector by a null signal. Null events represent the straightforward demonstration of the quantum Zeno paradox. Also, high probability of survival was demonstrated when the ion, driven by a fractionated $π$ pulse, was probed {\em and monitored} during the…
Zeno and Anti-Zeno Effects in Dark-State Dynamics Under Thermal Dephasing: A Numerical Study
通过Lindblad主方程数值模拟，研究腔QED系统中热退相干导致的测量诱导退相干对暗态稳定性的Zeno和反Zeno效应，发现低退相干强度下测量加速暗态退相干（反Zeno区），高强度下减缓并部分恢复暗态（Zeno区）。
In this paper, we systematically study the spontaneous decay phenomenon of a two-level system under the influences of both its environment and continuous measurements. In order to clarify some well-established conclusions about the quantum Zeno effect (QZE) and the quantum anti-Zeno effect (QAZE), we do not use the rotating wave approximation (RWA) in obtaining an effective Hamiltonian. We examine various spectral distributions by making use of our present approach in comparison with other approaches. It is found that with respect to a bare excited state even without the RWA, the QAZE can stil…
Non-Markovian Collective Emission of Giant emitters in the Zeno Regime
本研究探究耦合至公共储库的巨型人造原子的集体芝诺动力学，揭示其集体辐射速率的平滑增长特性、不同构型差异及超辐射方向性等，拓展了巨型原子集体辐射研究领域。
By using quantum Zeno dynamics, we propose a controllable approach to deterministically generate tripartite GHZ states for three atoms trapped in spatially separated cavities. The nearest-neighbored cavities are connected via optical fibers and the atoms trapped in two ends are tunably driven. The generation of the GHZ state can be implemented by only one step manipulation, and the EPR entanglement between the atoms in two ends can be further realized deterministically by Von Neumann measurement on the middle atom. Note that the duration of the quantum Zeno dynamics is controllable by switchin…
We propose an adiabatic passage approach to generate two atoms three- dimensional entanglement with the help of quantum Zeno dynamics in a time- dependent interacting field. The atoms are trapped in two spatially separated cavi- ties connected by a fiber, so that the individual addressing is needless. Because the scheme is based on the resonant interaction, the time required to generate entangle- ment is greatly shortened. Since the fields remain in vacuum state and all the atoms are in the ground states, the losses due to the excitation of photons and the spon- taneous transition of atoms are…
We study the measurement-induced enhancement of the spontaneous decay (called quantum anti-Zeno effect) for a two-level subsystem, where measurements are treated as couplings between the excited state and an auxiliary state rather than the von Neumann's wave function reduction. The photon radiated in a fast decay of the atom, from the auxiliary state to the excited state, triggers a quasi-measurement, as opposed to a projection measurement. Our use of the term "quasi-measurement" refers to a "coupling-based measurement". Such frequent quasi-measurements result in an exponential decay of the su…
We investigate the Zeno dynamics of quantum chirps. More specifically, we analyze the Zeno dynamics of a chirped solitary wave solution of the non-dimensional nonlinear Schrödinger equation (NLSE) with a gain/loss term. We show that the motion of the quantum chirp can be inhibited by frequent measurements in the observation domain. In order to assess the effect of Zeno dynamics on the quantum chirp imaging resolution, we analyze and compare its point spread functions (PSF) under free evolution and under Zeno dynamics. Additionally, we investigate the effect of observation frequency on the quan…
We consider an ensemble of atoms with $Λ$-type level structure trapped in a single-mode cavity, and propose a geometric scheme of coherent manipulation of quantum states on the subspace of zero-energy states within the quantum Zeno subspace of the system. We find that the particular subspace inherits the decoherence-free nature of the quantum Zeno subspace and features a symmetry-protected degeneracy, fulfilling all the conditions for a universal scheme of arbitrary unitary operations on it.
Eluding Zeno effect via dephasing and detuning
本文提出通过引入相移和失谐的观测方式，使频繁测量不再阻止系统从初态经中间态到达末态，从而规避芝诺效应，并证明该方法可推广至谐振子链和原子能级等多种量子系统。
Low-contrast all-optical Zeno switching has been demonstrated in a silicon nitride microdisk resonator coupled to a hot atomic vapor. The device is based on the suppression of the field build-up within a microcavity due to non-degenerate two-photon absorption. This experiment used one beam in a resonator and one in free-space due to limitations related to device physics. These results suggest that a similar scheme with both beams resonant in the cavity would correspond to input power levels near 20 nW.
Short pulses of a probe laser have been used in the past to measure whether a two-level atom is in its ground or excited state. The probe pulse couples the ground state to a third, auxiliary, level of the atom. Occurrence or absence of resonance fluorescence were taken to mean that the atom was found in its ground or excited state, respectively. In this paper we investigate to what extent this procedure results in an effective measurement to which the projection postulate can be applied, at least approximately. We discuss in detail the complications arising from an additional time development …
The quantum Zeno and anti-Zeno paradigms have thus far addressed the evolution control of a quantum system coupled to an immutable bath via non-selective measurements performed at appropriate intervals. We fundamentally modify these paradigms by introducing, theoretically and experimentally, the concept of controlling the bath state via selective measurements of the system (a qubit). We show that at intervals corresponding to the anti-Zeno regime of the system-bath exchange, a sequence of measurements has strongly correlated outcomes. These correlations can dramatically enhance the bath-state …
Developing quantum machines which can outperform their classical counterparts, thereby achieving quantum supremacy or quantum advantage, is a major aim of the current research on quantum thermodynamics and quantum technologies. Here we show that a fast-modulated cyclic quantum heat machine operating in the non-Markovian regime can lead to significant heat-current and power boosts induced by the anti-Zeno effect. Such boosts signify a quantum advantage over almost all heat-machines proposed thus far that operate in the conventional Markovian regime, where the quantumness of the system-bath inte…
We consider inter-atomic forces due to resonant dipole-dipole interactions within a dimer of highly excited Rydberg atoms, embedded in an ultra-cold gas. These forces rely on a coherent superposition of two-atom electronic states, which is destroyed by continuous monitoring of the dimer state through a detection scheme utilizing controllable interactions with the background gas atoms. We show that this intrinsic decoherence of the molecular energy surface can gradually deteriorate a repulsive dimer state, causing a mixing of attractive and repulsive character. For sufficiently strong decoheren…
In this paper, we study a quantum anti-Zeno effect (QAZE) purely induced by repetitive measurements for an artificial atom interacting with a structured bath. This bath can be artificially realized with coupled resonators in one dimension and possesses photonic band structure like Bloch electron in a periodic potential. In the presence of repetitive measurements, the pure QAZE is discovered as the observable decay is not negligible even for the atomic energy level spacing outside of the energy band of the artificial bath. If there were no measurements, the decay would not happen outside of the…
We show how engineered classical noise can be used to generate constrained Hamiltonian dynamics in atomic quantum simulators of many-body systems, taking advantage of the continuous Zeno effect. After discussing the general theoretical framework, we focus on applications in the context of lattice gauge theories, where imposing exotic, quasi-local constraints is usually challenging. We demonstrate the effectiveness of the scheme for both Abelian and non-Abelian gauge theories, and discuss how engineering dissipative constraints substitutes complicated, non-local interaction patterns by global c…
Quantum Zeno Effect in the Spatial Evolution of a Single Atom
该研究利用光学偶极阱对自由空间单原子进行投影测量，实验揭示量子芝诺效应及测量反作用动力学，并实现运动态制备与无额外动量的定向输运。
The behavior displayed by a quantum system when it is perturbed by a series of von Neumann measurements along time is analyzed. Because of the similarity between this general process with giving a deck of playing cards a shuffle, here it is referred to as quantum shuffling, showing that the quantum Zeno and anti-Zeno effects emerge naturally as two time limits. Within this framework, a connection between the gradual transition from anti-Zeno to Zeno behavior and the appearance of an underlying Markovian dynamics is found. Accordingly, although a priori it might result counterintuitive, the qua…
A scheme is presented for protecting one-qubit quantum information against decoherence due to a general environment and local exchange interactions. The scheme operates essentially by distributing information over two pairs of qubits and through error prevention procedures. In the scheme, quantum information is encoded through a decoherence-free subspace for collective phase errors and exchange errors affecting the qubits in pairs; leakage out of the encoding space due to amplitude damping is reduced by quantum Zeno effect. In addition, how to construct decoherence-free states for n-qubit info…
Measurement is one of the most counter-intuitive aspects of quantum physics. Frequent measurements of a quantum system lead to quantum Zeno dynamics where time evolution becomes confined to a subspace defined by the projections. However, weak measurement performed at a finite rate is also capable of locking the system into such a Zeno subspace in an unconventional way: by Raman-like transitions via virtual intermediate states outside this subspace, which are not forbidden. Here, we extend this concept into the realm of non-Hermitian dynamics by showing that the stochastic competition between m…
We present a convenient and efficient way to exchange and distribute multipartite entangled state via atomic coherence induced by electromagnetically induced transparency (EIT) in an atomic ensemble. By using the EIT-based nondegenerate four-wave mixing processes, the generation, exchange, and distribution of light-light, atom-light, and atom-atom multipartite entanglement can be achieved in a deterministic way with only coherent light fields. This EIT-induced atomic coherence acts as a quantum information processor and has the function of quantum beam splitter, quantum frequency converter, qu…
We demonstrate the control of quantum tunneling in an ultracold lattice gas by the measurement backaction imposed by an imaging process. A {\em in situ} imaging technique is used to acquire repeated images of an ultracold gas confined in a shallow optical lattice. The backaction induced by these position measurements modifies the coherent quantum tunneling of atoms within the lattice. By smoothly varying the rate at which spatial information is extracted from the atomic ensemble, we observe the continuous crossover from the 'weak measurement regime' where position measurements have little infl…
Photon-photon interactions mediated by an atomic gas can effect efficient polarization exchanges between two beams, leaving the medium exactly in its initial state. In, e.g., hydrogen, the distance required for macroscopic exchange is of order one tenth the distance in which the ordinary non-linear index of refraction would induce a phase change of pi. Several examples are worked out that show the variety of behaviors that can result, depending on the initial respective polarizations stated and the angle between the beams. Of particular interest are initial conditions in which there is no exch…
We suggest an application of dynamical Zeno effect to isolate a qubit in the quantum memory unit against decoherence caused by coupling with the reservoir having zero temperature. The method is based on using an auxiliary casing system that mediate the qubit-reservoir interaction and is simultaneously frequently erased to ground state. This screening procedure can be implemented in the cavity QED experiments to store the atomic and photonic qubit states.
Promising access to high-speed quantum networks relies on the creation of high-dimensional entangled memories that provide quantum communication with higher capacity of noisy quantum channels, thereby reducing the transmission time of information. Yet, the distribution of multidimensional entanglement between remote memory nodes is still faintly investigated. We propose an experimentally feasible protocol of deterministic generation of high-dimensional entanglement between distant multi-level atoms confined in high-finesse optical cavities and driven by laser pulses. Three-dimensional entangle…
Kondo-Zeno crossover in the dynamics of a monitored quantum dot
本文研究受监测量子点的近藤-芝诺交叉：通过持续监测量子点总电荷，发现初始极化自旋衰减率从近藤屏蔽（相互作用控制）转变为量子芝诺效应（随监测率增加而降低），长寿命近藤态对弱耗散鲁棒，推导了弱耗散下的非厄米近藤有效模型。
Cycling processes are important in many areas of physics ranging from lasers to topological insulators, often offering surprising insights into dynamical and structural aspects of the respective system. Here we report on a quantum-nonlinear wave-mixing experiment where resonant lasers and an optical cavity define a closed cycle between several ground and excited states of a single atom. We show that, for strong atom-cavity coupling and steady-state driving, the entanglement between the atomic states and intracavity photon number suppresses the excited-state population via quantum interference,…
Photon Anomalous Blockade in Waveguide Cavity QED with Atomic Mirrors
本文研究了波导腔量子电动力学系统中输出场的光子统计特性，发现即使在损耗大、耦合弱的波导腔中，光子阻塞现象仍可能发生，这与传统光子阻塞或非传统量子干涉在腔QED系统中的条件不同。通过主方程和散射理论推导了弱驱动系统中光子阻塞的条件，发现这种异常光子阻塞是由量子芝诺效应引起的，并且对腔内介质原子位置的变化具有鲁棒性。
Interaction-Assisted Spin Coherence in a Multimode Trapped Atomic Ensemble
本文研究多模囚禁原子系综中热占据导致的拉姆齐对比度衰减，提出弱轴分辨哈密顿理论，发现交换相互作用可恢复集体相干性，且交叉耦合遵循逆平方热标度。
Nuclear Spin Squeezing Based on Spin-Exchange Collisions
本研究基于碱金属与惰性气体系综的相干自旋交换相互作用，提出一种可高效制备操控超长寿命核自旋压缩的方案，该方案易实现且适配性高，将推动核自旋非经典态的相关研究与应用。
Real quantum measurements almost always cause a much stronger back action than required by the laws of quantum mechanics. In particular, free-space optical detection methods for single atoms and ions such as the shelving technique, though being among the most sensitive detection methods in quantum physics, inevitably require spontaneous scattering, even in the dispersive regime. This causes heating, a limitation for atom-based quantum information processing where it obviates straightforward reuse of the qubit. No such energy exchange is required by quantum mechanics. Here we experimentally dem…
Long-range dipole-dipole exchange-induced atomic grating
本文提出一种基于超冷铷原子系综与可移动里德伯自旋原子的偶极交换诱导光栅方案，利用自旋原子空间位置动态调控电磁诱导光栅，为光栅调控提供新途径。
Generalized Zeno effect and entanglement dynamics induced by fermion counting
本文研究自由费米子在粒子计数测量下的纠缠动力学，结合量子轨迹模拟与复本 Keldysh 场论，揭示其与局域占据测量共享广义芝诺效应及有限共形临界区间。
We first devise a scheme to perform a universal entangling gate via controlled collisions between pairs of atomic qubits trapped with optical tweezers. Second, we present a modification to this scheme to allow the preparation of atomic Bell pairs via selective excitation, suitable for quantum information processing applications that do not require universality. Both these schemes are enabled by the inherent symmetries of identical composite particles, as originally proposed by Hayes et al. Our scheme provides a technique for producing weighted graph states, entangled resources for quantum comm…
We propose to realize a passive optical quantum swapping device which allows for the exchange of the quantum fluctuations of two bright optical fields interacting with a coherent atomic medium in an optical cavity. The device is based on a quantum interference process between the fields within the cavity bandwidth arising from coherent population trapping in the atomic medium.
Hartree-Fock atom in a strong electric static field is considered. It is demonstrated that exchange between outer and inner electrons, taken into account by the so-called Fock term affects strongly the long-range behavior of the inner electron wave function. As a result, it dramatically increases its probability to be ionized. A simple model is analyzed demonstrating that the decay probability, compared to the case of a local (Hartree) atomic potential, increases by many orders of magnitude. As a result of such increase, the ratio of inner to outer electrons ionization probability became not t…
We propose an experimental realisation of the protocol for the counterfactual disembodied transport of an unknown qubit -- or what we call counterportation -- where sender and receiver, remarkably, exchange no particles. We employ cavity quantum electrodynamics, estimating resources for beating the classical fidelity limit -- except, unlike teleportation, no pre-shared entanglement nor classical communication are required. Our approach is multiple orders of magnitude more efficient in terms of physical resources than previously proposed implementations, paving the way for a demonstration using…
We present a scheme for creating quantum entangled atomic states through the coherent spin-exchange collision of a spinor Bose-Einstein condensate. The state generated possesses macroscopic Einstein-Podolsky-Roson correlation and the fluctuation in one of its quasi-spin components vanishes. We show that an elongated condensate with large aspect ratio is most suitable for creating such a state.
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