Plasmonic Dicke effect

We study cooperative emission by an ensemble of emitters, such as fluorescing molecules or semiconductor quantum dots, near a metal nanoparticle. The primary mechanism of cooperative emission is resonant energy transfer between emitters and plasmons rather than Dicke radiative coupling between emitters. The emission is dominated by three superradiant states with the same quantum yield as a single emitter, leading to a drastic reduction of ensemble radiated energy down to just thrice of that by a single emitter, the remaining energy being dissipated in the metal through subradiant states. We perform numerical calculations of system eigenstates and find that the plasmonic Dicke effect interactions affect is not impacted by the interactions between emitters or non-radiative losses in the metal.     

Product-State Approximations to Quantum States

We show that for any many-body quantum state there exists an unentangled quantum state such that most of the two-body reduced density matrices are close to those of the original state. This is a statement about the monogamy of entanglement, which cannot be shared without limit in the same way as classical correlation. Our main application is to Hamiltonians that are sums of two-body terms. For such Hamiltonians we show that there exist product states with energy that is close to the ground-state energy whenever the interaction graph of the Hamiltonian has high degree. This proves the validity of mean-field theory and gives an explicitly bounded approximation error. If we allow states that are entangled within small clusters of systems but product across clusters then good approximations exist when the Hamiltonian satisfies one or more of the following properties: (1) high degree, (2) small expansion, or (3) a ground state where the blocks in the partition have sublinear entanglement. Previously this was known only in the case of small expansion or in the regime where the entanglement was close to zero. Our approximations allow an extensive error in energy, which is the scale considered by the quantum PCP (probabilistically checkable proof) and NLTS (no low-energy trivial-state) conjectures. Thus our results put restrictions on the possible Hamiltonians that could be used for a possible proof of the qPCP or NLTS conjectures. By contrast the classical PCP constructions are often based on constraint graphs with high degree. Likewise we show that the parallel repetition that is possible with classical constraint satisfaction problems cannot also be possible for quantum Hamiltonians, unless qPCP is false. The main technical tool behind our results is a collection of new classical and quantum de Finetti theorems which do not make any symmetry assumptions on the underlying states.     

Superradiant emission dynamics of an optically thin material sample in a short-decay-time optical cavity

We report observations of optical superradiant emission and the atomic evolution it drives under conditions closely approximating those originally envisioned in the classic work of Dicke [Phys. Rev. 93, 99 (1954)]. Our experiment involves an optically thin solid sample in a short-lifetime optical cavity whose homogeneous coherence is cryogenically stabilized. Pulsed coherent excitation initiates superradiant emission which subsequently drives the sample to higher or lower states of coherence. Suppression of dephasing via cryogenics and propagation effects through use of an optically thin sample and cavity provides one of the clearest and cleanest examples of Dicke superradiance yet reported.     

Superradiance of a degenerate exciton gas in semiconductors with indirect fundamental absorption edge

It is predicted that superradiant states can be formed in a degenerate exciton gas in a semiconductor with an indirect fundamental absorption edge. The superradiance results from four-particle recombination processes and occurs at photon energies approximately twice as high as the band gap energy. Experimental results supporting the possibility of the observation of superradiance from SiGe/Si quantum wells are presented.     

Energy convexity as a consequence of decoherence and pair-extensive interactions in many-electron systems

Using the concept of self-entanglement, through which a pure state constructed in an augmented Hilbert space can describe a mixed state and through which the effects of physical decoherence can be mapped onto systems separated by an infinite distance, with the role of environmental states assumed by system states in disjoint Hilbert spaces, we show that expectation values of Hamiltonians subscribing to decoherence and satisfying the condition of extensivity, defined in the text, obey the energy convexity relation. The analysis based on self-entanglement also leads to a surprising interpretation of the failure of the convexity relation for model Hamiltonians such as the Hubbard model: The failure is due to the existence of self-entangled states with lower energies than the ground state so that in such models decoherence, i.e., disentangling from the self-entangled states, would cost energy and disallow the observation of the state through measurement. The Hubbard model is discussed extensively in an appendix where we also discuss and resolve some of the counterarguments to the convexity relation that have been advanced in the literature.     

Information storage capacity of discrete spin systems

Understanding the limits imposed on information storage capacity of physical systems is a problem of fundamental and practical importance which bridges physics and information science. There is a well-known upper bound on the amount of information that can be stored reliably in a given volume of discrete spin systems which are supported by gapped local Hamiltonians. However, all the previously known systems were far below this theoretical bound, and it remained open whether there exists a gapped spin system that saturates this bound. Here, we present a construction of spin systems which saturate this theoretical limit asymptotically by borrowing an idea from fractal properties arising in the Sierpinski triangle. Our construction provides not only the best classical error-correcting code which is physically realizable as the energy ground space of gapped frustration-free Hamiltonians, but also a new research avenue for correlated spin phases with fractal spin configurations.     

Quantum Systems Connected by a Time-Dependent Canonical Transformation

We study both classical and quantum relation between two Hamiltoniansystems which are mutually connected by time-dependent canonical transformation. One is ordinary conservative system and the other istime-dependent Hamiltonian system. The quantum unitary operatorrelevant to classical canonical transformation between the two systems are obtained through rigorous evaluation. With the aid of the unitary operator, we have derived quantum states of the time-dependent Hamiltonian system through transforming the quantum states of the conservative system. The invariant operators of the two systems are presented and the relation between them are addressed. We showed that there exist numerous Hamiltonians, which gives the same classical equation of motion. Though it is impossible to distinguish the systems described by these Hamiltonians within the realm of classical mechanics, they can be distinguishable quantum mechanically.     

A family of affine quantum group invariant integrable extensions of the Hubbard Hamiltonian

We construct a family of spin chain Hamiltonians, which have the affine quantum group symmetry . Their eigenvalues coincide with the eigenvalues of the usual spin chain Hamiltonians, but have the degeneracy of levels, corresponding to the affine . The space of states of these spin chains is formed by the tensor product of the fully reducible representations of the quantum group.

The fermionic representations of the constructed spin chain Hamiltonians show that we have obtained new extensions of the Hubbard Hamiltonians. All of them are integrable and have the affine quantum group symmetry. The exact ground state of such type of model is presented, exhibiting superconducting behavior via the η-pairing mechanism.     

光腔中两组分玻色-爱因斯坦凝聚体的受激辐射特性和量子相变

研究了单模光腔中两组分玻色-爱因斯坦凝聚的基态性质和相关的量子相变.通过利用自旋相干态变换将等效赝自旋哈密顿算符对角化并求得基态能量泛函.基态能量泛函对其经典场变量进行变分并取极小值,得到光子数解和相边界曲线.通过稳定性讨论发现系统除了出现正常相和超辐射相之外,还得到了多稳的宏观量子态;受激辐射来自于原子数反转的集体态,单组分的Dicke系统中并没有此现象;受激辐射只能从一组分的原子中产生,而另外的仍保持在普通超辐射状态.通过调整相关的原子-场耦合强度和频率失谐,超辐射和受激辐射态的顺序可以在原子的两个组分之间互换.     

Classification of quantum phases and topology of logical operators in an exactly solved model of quantum codes

Searches for possible new quantum phases and classifications of quantum phases have been central problems in physics. Yet, they are indeed challenging problems due to the computational difficulties in analyzing quantum many-body systems and the lack of a general framework for classifications. While frustration-free Hamiltonians, which appear as fixed point Hamiltonians of renormalization group transformations, may serve as representatives of quantum phases, it is still difficult to analyze and classify quantum phases of arbitrary frustration-free Hamiltonians exhaustively. Here, we address these problems by sharpening our considerations to a certain subclass of frustration-free Hamiltonians, called stabilizer Hamiltonians, which have been actively studied in quantum information science. We propose a model of frustration-free Hamiltonians which covers a large class of physically realistic stabilizer Hamiltonians, constrained to only three physical conditions; the locality of interaction terms, translation symmetries and scale symmetries, meaning that the number of ground states does not grow with the system size. We show that quantum phases arising in two-dimensional models can be classified exactly through certain quantum coding theoretical operators, called logical operators, by proving that two models with topologically distinct shapes of logical operators are always separated by quantum phase transitions.     

Quantum codes give counterexamples to the unique preimage conjecture of the N-representability problem

It is well known that the ground state energy of many-particle Hamiltonians involving only 2-body interactions can be obtained using constrained optimizations over density matrices which arise from reducing an N-particle state. While determining which 2-particle density matrices are "N-representable" is a computationally hard problem, all known extreme N-representable 2-particle reduced density matrices arise from a unique N-particle preimage, satisfying a conjecture established in 1972. We present explicit counterexamples to this conjecture through giving Hamiltonians with 2-body interactions which have degenerate ground states that cannot be distinguished by any 2-body operator. We relate the existence of such counterexamples to quantum error correction codes and topologically ordered spin systems.     

On the correspondence between fermion and boson states and operators

Mapping of shell-model (fermion) Hamiltonians onto boson Hamiltonians which underly the interaction boson model ^1–5) is investigated. A simple correspondence is defined and a sufficient condition given for shell-model Hamiltonians to simply correspond to finite hermitian boson Hamiltonians. A special case is discussed where diagonalization of a shell-model Hamiltonian for valence protons and neutrons can be exactly carried out in an equivalent (but different) boson space. If, however, the proton Hamiltonian and neutron Hamiltonian are diagonal in the seniority scheme, mapping of fermion states onto orthogonal boson states cannot be a simple correspondence. In that case the boson quadrupole operators equivalent to fermion guadrupole operators cannot be single-boson operators but must be more complicated, ones.     

Superradiance and subradiance in an inhomogeneously broadened ensemble of two-level systems coupled to a low-Q cavity

The collective spontaneous emission of a fully inverted inhomogeneously broadened ensemble of N two-level systems coupled to a single-mode low-Q cavity is investigated numerically using Monte Carlo wave function technique. An intrinsically bi-exponential emission dynamics is found when the time scales of superradiance tau(sr) and inhomogeneous dephasing T2* approximately 1/Deltaomega(inh) become comparable: a fast superradiant is followed by a slow subradiant decay. Experimental configurations using ensembles of quantum dots coupled to optical microcavities are proposed as possible candidates to observe the combined superradiant and subradiant energy relaxation.     

Quantum simulation of time-dependent Hamiltonians and the convenient illusion of Hilbert space

We consider the manifold of all quantum many-body states that can be generated by arbitrary time-dependent local Hamiltonians in a time that scales polynomially in the system size, and show that it occupies an exponentially small volume in Hilbert space. This implies that the overwhelming majority of states in Hilbert space are not physical as they can only be produced after an exponentially long time. We establish this fact by making use of a time-dependent generalization of the Suzuki-Trotter expansion, followed by a well-known counting argument. This also demonstrates that a computational model based on arbitrarily rapidly changing Hamiltonians is no more powerful than the standard quantum circuit model.     

Superradiant cascade emissions in an atomic ensemble via four-wave mixing

We investigate superradiant cascade emissions from an atomic ensemble driven by two-color classical fields. The correlated pair of photons (signal and idler) is generated by adiabatically driving the system with large-detuned light fields via four-wave mixing. The signal photon from the upper transition of the diamond-type atomic levels is followed by the idler one which can be superradiant due to light-induced dipole–dipole interactions. We then calculate the cooperative Lamb shift (CLS) of the idler photon, which is a cumulative effect of interaction energy. We study its dependence on a cylindrical geometry, a conventional setup in cold atom experiments, and estimate the maximum CLS which can be significant and observable. Manipulating the CLS of cascade emissions enables frequency qubits that provide alternative robust elements in quantum network.     

Effects of Isospin on Pre-scission Particle Multiplicity of Heavy Systems and Its Excitation Energy Dependence

Isospin effects on particle emission of fissioning isobaric sources ²⁰²Fr, ²⁰²Po, ²⁰²Tl and isotopic sources ^189,202,212Po, and its dependence on the excitation energy are studied via Smoluchowski equations. It is shown that with increasing the isospin of fissioning systems, charged-particle emission is not sensitive to the strength of nuclear dissipation. In addition, we have found that increasing the excitation energy not only increases the influence of nuclear dissipation on particle emission but also greatly enhances the sensitivity of the emission of pre-scission neutrons or charged particles to the isospin of the system. Therefore, in order to extract dissipation strength more accurately by taking light particle multiplicities it is important to choose both a highly excited compound nucleus and a proper kind of particles for systems with different isospins.     

Vibration analog of a superradiant quantum transition

A vibrational analog of the superradiant quantum transition (SQT) in a classical system of weakly bound oscillators of van der Pole-Duffing (self-generators), in which the coupling element is a linear oscillator, is described. Such an analog is a strongly modulated oscillatory process of almost complete periodic energy exchange between the generators. This type of mode is alternative to nonlinear normal modes (NNM) and close in its character to limiting phase trajectories (LPTs), which have been introduced recently as applied to conservative systems, but in contrast to them, as the attractor. It is shown that the necessary condition of the transition to intense energy exchange in the classical system is the instability of one of the NNMs similarly to that when the condition of the superradiant transition is the instability of the ground state in a quantum model.     

比容可分性及其在自由电子气体模型中的应用

 在巨正则统计系综中获得了系统比容可按哈密顿组成拆分的两类系统,即哈密顿完全可分或相互间存在联系的子系统的化学势可由相应的自由能得到。在此基础上讨论了金属自由电子近似模型中热电子对比容的贡献,并给出了相应的吴-经参数。     

Avoided level crossings and singular points

Avoided crossings of discrete states as well as of resonance states are traced back to the existence of branch points (BPs) which are singular points in the complex energy plane. They cannot be identified with exceptional points. At a BP width bifurcation occurs, different Riemann sheets evolve and the levels do not cross anymore when the system is still further opened. The BPs are physically meaningful: they influence the dynamics of open as well as of closed quantum systems. The geometric phase that arises by encircling a BP, is different from the phase that appears by encircling a diabolic point. This is found to be true even for the two BPs into which the diabolic point is unfolded by opening the system. Presented at the 3rd International Workshop “Pseudo-Hermitian Hamiltonians in Quantum Physics”, Istanbul, Turkey, June 20–22, 2005.