Beyond optical molasses: 3D raman sideband cooling of atomic cesium to high phase-space density

In Situ Imaging of a Single-Atom Wave Packet in Continuous Space

We report on the imaging of the in situ spatial distribution of deterministically prepared single-atom wave packets as they expand in a plane, finding excellent agreement with the scaling dynamics predicted by the Schrödinger equation. Our measurement provides a direct and quantitative observation of the textbook free expansion of a one-particle Gaussian wave packet, which we believe has no equivalent in the existing literature. Second, we utilize these expanding wave packets as a benchmark to develop a protocol for the controlled projection of a spatially extended wave function from continuous space onto the sites of a deep optical lattice and subsequent single-atom imaging using quantum gas microscopy techniques. By probing the square modulus of the wave function for various lattice ramp-up times, we show how to obtain a near-perfect projection onto lattice sites. Establishing this protocol represents a crucial prerequisite to the realization of a quantum gas microscope for continuum physics. The method demonstrated here for imaging a wave packet whose initial extent greatly exceeds the pinning lattice spacing, is designed to be applicable to the many-body wave function of interacting systems in continuous space, promising a direct access to their microscopic properties, including spatial correlation functions up to high order and large distances.

Bose-Einstein Condensation by Polarization Gradient Laser Cooling

Attempts to create quantum degenerate gases without evaporative cooling have been pursued since the early days of laser cooling, with the consensus that polarization gradient cooling (PGC, also known as "optical molasses") alone cannot reach condensation. In the present work, we report that simple PGC can generate a small Bose-Einstein condensate (BEC) inside a corrugated micrometer-sized optical dipole trap. The experimental parameters enabling BEC creation were found by machine learning, which increased the atom number by a factor of 5 and decreased the temperature by a factor of 2.5, corresponding to almost 2 orders of magnitude gain in phase space density. When the trapping light is slightly misaligned through a microscopic objective lens, a BEC of ∼250 ^{87}Rb atoms is formed inside a local dimple within 40 ms of PGC after MOT loading.

Bose-Einstein condensation of non-ground-state caesium atoms

Bose-Einstein condensates of ultracold atoms serve as low-entropy sources for a multitude of quantum-science applications, ranging from quantum simulation and quantum many-body physics to proof-of-principle experiments in quantum metrology and quantum computing. For stability reasons, in the majority of cases the energetically lowest-lying atomic spin state is used. Here, we report the Bose-Einstein condensation of caesium atoms in the Zeeman-excited mf = 2 state, realizing a non-ground-state Bose-Einstein condensate with tunable interactions and tunable loss. We identify two regions of magnetic field in which the two-body relaxation rate is low enough that condensation is possible. We characterize the phase transition and quantify the loss processes, finding unusually high three-body losses in one of the two regions. Our results open up new possibilities for the mixing of quantum-degenerate gases, for polaron and impurity physics, and in particular for the study of impurity transport in strongly correlated one-dimensional quantum wires.

Indication of critical scaling in time during the relaxation of an open quantum system

Near continuous phase transitions, universal power-law scaling, characterized by critical exponents, emerges. This behavior reflects the singular responses of physical systems to continuous control parameters like temperature or external fields. Universal scaling extends to non-equilibrium dynamics in isolated quantum systems after a quench, where time takes the role of the control parameter. Our research unveils critical scaling in time also during the relaxation dynamics of an open quantum system. Here we experimentally realize such a system by the spin of individual Cesium atoms dissipatively coupled through spin-exchange processes to a bath of ultracold Rubidium atoms. Through a finite-size scaling analysis of the entropy dynamics via numerical simulations, we identify a critical point in time in the thermodynamic limit. This critical point is accompanied by the divergence of a characteristic length, which is described by critical exponents that turn out to be unaffected by system specifics.

Design and construction of a quantum matter synthesizer

The quantum matter synthesizer (QMS) is a new quantum simulation platform in which individual particles in a lattice can be resolved and re-arranged into arbitrary patterns. The ability to spatially manipulate ultracold atoms and control their tunneling and interactions at the single-particle level allows full control of a many-body quantum system. We present the design and characterization of the QMS, which integrates into a single ultra-stable apparatus a two-dimensional optical lattice, a moving optical tweezer array formed by a digital micromirror device, and site-resolved atomic imaging. We demonstrate excellent mechanical stability between the lattice and tweezer array with relative fluctuations below 10 nm, diffraction-limited imaging at a resolution of 655 nm, and high-speed real-time control of the tweezer array at a 2.52 kHz refresh rate, which will be adopted to realize fast rearrangement of atoms. The QMS also features new technologies and schemes, such as nanotextured anti-reflective windows and all-optical long-distance transport of atoms.

Atom-optically synthetic gauge fields for a noninteracting Bose gas

Synthetic gauge fields in synthetic dimensions are now of great interest. This concept provides a convenient manner for exploring topological phases of matter. Here, we report on the first experimental realization of an atom-optically synthetic gauge field based on the synthetic momentum-state lattice of a Bose gas of ¹³³Cs atoms, where magnetically controlled Feshbach resonance is used to tune the interacting lattice into noninteracting regime. Specifically, we engineer a noninteracting one-dimensional lattice into a two-leg ladder with tunable synthetic gauge fields. We observe the flux-dependent populations of atoms and measure the gauge field-induced chiral currents in the two legs. We also show that an inhomogeneous gauge field could control the atomic transport in the ladder. Our results lay the groundwork for using a clean noninteracting synthetic momentum-state lattice to study the gauge field-induced topological physics.

Hybrid evaporative cooling of 133Cs atoms to Bose-Einstein condensation

The Bose-Einstein condensation (BEC) of ¹³³Cs atoms offers an appealing platform for studying the many-body physics of interacting Bose quantum gases, owing to the rich Feshbach resonances that can be readily achieved in the low magnetic field region. However, it is notoriously difficult to cool ¹³³Cs atoms to their quantum degeneracy. Here we report a hybrid evaporative cooling of ¹³³Cs atoms to BEC. Our approach relies on a combination of the magnetically tunable evaporation with the optical evaporation of atoms in a magnetically levitated optical dipole trap overlapping with a dimple trap. The magnetic field gradient is reduced for the magnetically tunable evaporation. The subsequent optical evaporation is performed by lowering the depth of the dimple trap. We study the dependence of the peak phase space density (PSD) and temperature on the number of atoms during the evaporation process, as well as how the PSD and atom number vary with the trap depth. The results are in excellent agreement with the equation model for evaporative cooling.

A quantum heat engine driven by atomic collisions

Quantum heat engines are subjected to quantum fluctuations related to their discrete energy spectra. Such fluctuations question the reliable operation of thermal machines in the quantum regime. Here, we realize an endoreversible quantum Otto cycle in the large quasi-spin states of Cesium impurities immersed in an ultracold Rubidium bath. Endoreversible machines are internally reversible and irreversible losses only occur via thermal contact. We employ quantum control to regulate the direction of heat transfer that occurs via inelastic spin-exchange collisions. We further use full-counting statistics of individual atoms to monitor quantized heat exchange between engine and bath at the level of single quanta, and additionally evaluate average and variance of the power output. We optimize the performance as well as the stability of the quantum heat engine, achieving high efficiency, large power output and small power output fluctuations.

Designing reliable nanoscale quantum-heat engines achieving high efficiency, high power and high stability is of fundamental and practical interest. Here, the authors report the realization of such a quantum machine using individual neutral Cs atoms in an atomic Rb bath, in which quantized heat exchange via inelastic spin-exchange collisions is controlled at the level of single quanta.

Strongly Correlated Quantum Gas Prepared by Direct Laser Cooling

We create a one-dimensional strongly correlated quantum gas of ^{133}Cs atoms with attractive interactions by direct laser cooling in 300 ms. After compressing and cooling the optically trapped atoms to the vibrational ground state along two tightly confined directions, the emergence of a non-Gaussian time-of-flight distribution along the third, weakly confined direction reveals that the system enters a quantum degenerate regime. We observe a reduction of two- and three-body spatial correlations and infer that the atoms are directly cooled into a highly correlated excited metastable state, known as a super-Tonks-Girardeau gas.

Direct Laser Cooling to Bose-Einstein Condensation in a Dipole Trap

We present a method for producing three-dimensional Bose-Einstein condensates using only laser cooling. The phase transition to condensation is crossed with 2.5×10^{4} ^{87}Rb atoms at a temperature of T_{c}=0.6  μK after 1.4 s of cooling. Atoms are trapped in a crossed optical dipole trap and cooled using Raman cooling with far-off-resonant optical pumping light to reduce atom loss and heating. The achieved temperatures are well below the effective recoil temperature. We find that during the final cooling stage at atomic densities above 10^{14}  cm^{-3}, careful tuning of trap depth and optical-pumping rate is necessary to evade heating and loss mechanisms. The method may enable the fast production of quantum degenerate gases in a variety of systems including fermions.

Steady-State Magneto-Optical Trap with 100-Fold Improved Phase-Space Density

We demonstrate a continuously loaded ^{88}Sr magneto-optical trap (MOT) with a steady-state phase-space density of 1.3(2)×10^{-3}. This is 2 orders of magnitude higher than reported in previous steady-state MOTs. Our approach is to flow atoms through a series of spatially separated laser cooling stages before capturing them in a MOT operated on the 7.4-kHz linewidth Sr intercombination line using a hybrid slower+MOT configuration. We also demonstrate producing a Bose-Einstein condensate at the MOT location, despite the presence of laser cooling light on resonance with the 30-MHz linewidth transition used to initially slow atoms in a separate chamber. Our steady-state high phase-space density MOT is an excellent starting point for a continuous atom laser and dead-time free atom interferometers or clocks.

Creation of a Bose-condensed gas of 87Rb by laser cooling

Protocols for attaining quantum degeneracy in atomic gases almost exclusively rely on evaporative cooling, a time-consuming final step associated with substantial atom loss. We demonstrate direct laser cooling of a gas of rubidium-87 (⁸⁷Rb) atoms to quantum degeneracy. The method is fast and induces little atom loss. The atoms are trapped in a two-dimensional optical lattice that enables cycles of compression to increase the density, followed by Raman sideband cooling to decrease the temperature. From a starting number of 2000 atoms, 1400 atoms reach quantum degeneracy in 300 milliseconds, as confirmed by a bimodal velocity distribution. The method should be broadly applicable to many bosonic and fermionic species and to systems where evaporative cooling is not possible.

Manipulation of photoassociation of ultracold Cs atoms with tunable scattering length by external magnetic fields

We demonstrate that for ultracold, optically trapped Cs atoms the photoassociation (PA) can be manipulated by using external uniform magnetic fields due to the alteration of the scattering wavefunction in the region of the free–bound optical transition. We present PA–induced atom loss measurements with the same intensity for PA laser but different external magnetic fields, and analyze main contributions of the PA to the variation of the number of atoms in the trap. The PA rate exhibits a strong dependence on the changing uniform magnetic field. The experimental data are simulated within the model of a single–channel one–well rectangular potential, whose depth is adjusted so as to assure the predicted variation of the scattering length with the magnetic field. The computational and experimental results are in a reasonable agreement to each other. The same model is used to illustrate some general properties of the two–body quantum system in the near–threshold state.

Observing Power-Law Dynamics of Position-Velocity Correlation in Anomalous Diffusion

In this Letter, we present a measurement of the phase-space density distribution (PSDD) of ultracold ^{87}Rb atoms performing 1D anomalous diffusion. The PSDD is imaged using a direct tomographic method based on Raman velocity selection. It reveals that the position-velocity correlation function C_{xv}(t) builds up on a time scale related to the initial conditions of the ensemble and then decays asymptotically as a power law. We show that the decay follows a simple scaling theory involving the power-law asymptotic dynamics of position and velocity. The generality of this scaling theory is confirmed using Monte Carlo simulations of two distinct models of anomalous diffusion.

Microscopic Observation of Pauli Blocking in Degenerate Fermionic Lattice Gases

The Pauli exclusion principle is one of the most fundamental manifestations of quantum statistics. Here, we report on its local observation in a spin-polarized degenerate gas of fermions in an optical lattice. We probe the gas with single-site resolution using a new generation quantum gas microscope avoiding the common problem of light induced losses. In the band insulating regime, we measure a strong local suppression of particle number fluctuations and a low local entropy per atom. Our work opens a new avenue for studying quantum correlations in fermionic quantum matter both in and out of equilibrium.

Measurement-Induced Localization of an Ultracold Lattice Gas

The process of measurement can modify the state of a quantum system and its subsequent evolution. Here, we demonstrate the control of quantum tunneling in an ultracold lattice gas by the measurement backaction imposed by the act of imaging the atoms, i.e., light scattering. By varying the rate of light scattering from the atomic ensemble, we show the crossover from the weak measurement regime, where position measurements have little influence on tunneling dynamics, to the strong measurement regime, where measurement-induced localization causes a large suppression of tunneling--a manifestation of the quantum Zeno effect. Our study realizes an experimental demonstration of the paradigmatic Heisenberg microscope and sheds light on the implications of measurement on the coherent evolution of a quantum system.

Site-resolved imaging of fermionic ^{6}Li in an optical lattice

We demonstrate site-resolved imaging of individual fermionic ^{6}Li atoms in a single layer of a 3D optical lattice. To preserve the density distribution during fluorescence imaging, we simultaneously cool the atoms with 3D Raman sideband cooling. This laser cooling technique, demonstrated here for the first time for ^{6}Li atoms, also provides a pathway to rapid low-entropy filling of an optical lattice. We are able to determine the occupation of individual lattice sites with a fidelity >95%, enabling direct, local measurement of particle correlations in Fermi lattice systems. This ability will be instrumental for creating and investigating low-temperature phases of the Fermi-Hubbard model, including antiferromagnets and d-wave superfluidity.

Quantum-gas microscope for fermionic atoms

We realize a quantum-gas microscope for fermionic ^{40}K atoms trapped in an optical lattice, which allows one to probe strongly correlated fermions at the single-atom level. We combine 3D Raman sideband cooling with high-resolution optics to simultaneously cool and image individual atoms with single-lattice-site resolution at a detection fidelity above 95%. The imaging process leaves the atoms predominantly in the 3D motional ground state of their respective lattice sites, inviting the implementation of a Maxwell's demon to assemble low-entropy many-body states. Single-site-resolved imaging of fermions enables the direct observation of magnetic order, time-resolved measurements of the spread of particle correlations, and the detection of many-fermion entanglement.

Suppression of ion transport due to long-lived subwavelength localization by an optical lattice

We report the localization of an ion by a one-dimensional optical lattice in the presence of an applied external force. The ion is confined radially by a radio frequency trap and axially by a combined electrostatic and optical-lattice potential. Using a resolved Raman sideband technique, one or several ions are cooled to a mean vibrational number <n>=(0.1±0.1) along the optical lattice. We measure the average position of a periodically driven ion with a resolution down to λ/40, and demonstrate localization to a single lattice site for up to 10 ms. This opens new possibilities for studying many-body systems with long-range interactions in periodic potentials, as well as fundamental models of friction.

Ground-state cooling of a single atom at the center of an optical cavity

A single neutral atom is trapped in a three-dimensional optical lattice at the center of a high-finesse optical resonator. Using fluorescence imaging and a shiftable standing-wave trap, the atom is deterministically loaded into the maximum of the intracavity field where the atom-cavity coupling is strong. After 5 ms of Raman sideband cooling, the three-dimensional motional ground state is populated with a probability of (89±2)%. Our system is the first to simultaneously achieve quantum control over all degrees of freedom of a single atom: its position and momentum, its internal state, and its coupling to light.

Coherence and Raman sideband cooling of a single atom in an optical tweezer

We investigate quantum control of a single atom in a tightly focused optical tweezer trap. We show that inevitable spatially varying polarization gives rise to significant internal-state decoherence but that this effect can be mitigated by an appropriately chosen magnetic bias field. This enables Raman sideband cooling of a single atom close to its three-dimensional ground state (vibrational quantum numbers n(x)=n(y)=0.01, n(z)=8) even for a trap beam waist as small as w=900  nm. The small atomic wave packet with δx=δy=24  nm and δz=270  nm represents a promising starting point for future hybrid quantum systems where atoms are placed in close proximity to surfaces.

3D projection sideband cooling

We demonstrate 3D microwave projection sideband cooling of trapped, neutral atoms. The technique employs state-dependent potentials that enable microwave photons to drive vibration-number reducing transitions. The particular cooling sequence we employ uses minimal spontaneous emission, and works even for relatively weakly bound atoms. We cool 76% of atoms to their 3D vibrational ground states in a site-resolvable 3D optical lattice.

Realization of an optomechanical interface between ultracold atoms and a membrane

We have realized a hybrid optomechanical system by coupling ultracold atoms to a micromechanical membrane. The atoms are trapped in an optical lattice, which is formed by retroreflection of a laser beam from the membrane surface. In this setup, the lattice laser light mediates an optomechanical coupling between membrane vibrations and atomic center-of-mass motion. We observe both the effect of the membrane vibrations onto the atoms as well as the backaction of the atomic motion onto the membrane. By coupling the membrane to laser-cooled atoms, we engineer the dissipation rate of the membrane. Our observations agree quantitatively with a simple model.

Off-resonance laser frequency stabilization using the Faraday effect

We present a simple technique for stabilization of a laser frequency off resonance using the Faraday effect in a heated vapor cell with an applied magnetic field. In particular, we demonstrate stabilization of a 780 nm laser detuned up to 14 GHz from the (85)Rb D(2) 5(2)S(1/2) F = 2 to 5(2)P(3/2) F' = 3 transition. Control of the temperature of the vapor cell and the magnitude of the applied magnetic field allows locking ~6-14 GHz red and blue detuned from the atomic line. We obtain an rms fluctuation of 7 MHz over 1 h without stabilization of the cell temperature or magnetic field.

Spectrum of two-level systems with discrete frequency fluctuations

We study, theoretically and experimentally, an ensemble of two-level systems coupled to an environment which induces random jumps in their resonant frequency. We present a closed-form formula for the spectrum in terms of the resonant frequency distribution and the Poisson rate constant. For a normal distribution the spectrum deviates from a generalized Gumbel function, a well-known result for continuous stochastic Gaussian processes. We perform experiments with optically trapped cold 87Rb atoms and show that the predictions of our theory for a 3D harmonic trap match the measured spectra without fitting parameters.

Microwave-Induced Cooling of a Superconducting Qubit

We demonstrated microwave-induced cooling in a superconducting flux qubit. The thermal population in the first-excited state of the qubit is driven to a higher-excited state by way of a sideband transition. Subsequent relaxation into the ground state results in cooling. Effective temperatures as low as approximately 3 millikelvin are achieved for bath temperatures of 30 to 400 millikelvin, a cooling factor between 10 and 100. This demonstration provides an analog to optical cooling of trapped ions and atoms and is generalizable to other solid-state quantum systems. Active cooling of qubits, applied to quantum information science, provides a means for qubit-state preparation with improved fidelity and for suppressing decoherence in multi-qubit systems.

Subkelvin Cooling NO Molecules via "Billiard-like" Collisions with Argon

We report the cooling of nitric oxide using a single collision between an argon atom and a molecule of NO. We have produced significant numbers (108 to 109 molecules per cubic centimeter per quantum state) of translationally cold NO molecules in a specific quantum state with an upper-limit root mean square laboratory velocity of 15 plus or minus 1 meters per second, corresponding to a 406 plus or minus 23 millikelvin upper limit of temperature, in a crossed molecular beam apparatus. The technique, which relies on a kinematic collapse of the velocity distributions of the molecular beams for the scattering events that produce cold molecules, is general and independent of the energy of the colliding partner.

Experiments with a 3D double optical lattice

We present a setup where we trap two different cesium hyperfine ground states in two different near-resonant optical lattices with identical topographies. We demonstrate that we can change the relative spatial phase between the lattices and we measure the equilibrium temperature as a function of the relative spatial phase. This provides a topographical chart of the optical potential. We also determine the rate at which atoms are transferred between the lattices and show that the setup is a promising candidate for implementing coherent quantum state manipulation.

Sensitive detection of cold cesium molecules formed on Feshbach resonances

We observe the dynamic formation of quasibound Cs2 molecules near Feshbach resonances in a cold sample of atomic cesium. Using an external probe beam, more than 15 weakly coupled molecular states are detected with high sensitivity, whose collisional formation cross sections are as small as sigma=2 x 10(-16) cm(2). By modeling the molecule formation and dissociation processes with rate equations, we conclude that at an atomic density of 10(13) cm(-3) and temperature of 5 microK, more than 5(1)x10(5) Cs2 molecules in a single rovibrational state coexist with 10(8) Cs atoms in our trap.

Bose-Einstein condensation of cesium

Bose-Einstein condensation of cesium atoms is achieved by evaporative cooling using optical trapping techniques. The ability to tune the interactions between the ultracold atoms by an external magnetic field is crucial to obtain the condensate and offers intriguing features for potential applications. We explore various regimes of condensate self-interaction (attractive, repulsive, and null interaction strength) and demonstrate properties of imploding, exploding, and non-interacting quantum matter.

Coherence with atoms

The past decade has seen dramatic progress in our ability to manipulate and coherently control the motion of atoms. This progress has both fundamental and applied importance. On the one hand, recent experiments are providing new perspectives for the study of quantum phase transitions and highly entangled quantum states. On the other hand, this exquisite control offers the prospect of a new generation of force sensors of unprecedented sensitivity and accuracy.

Producing Bose-Einstein condensates using optical lattices

We relate the entropies of ensembles of atoms in optical lattices to atoms in simple traps. We then determine which ensembles of lattice-bound atoms will adiabatically transform into a Bose condensate. This shows a feasible approach to Bose condensation without evaporative cooling.

Sympathetic cooling with two atomic species in an optical trap

We simultaneously trap ultracold lithium and cesium atoms in an optical dipole trap formed by the focus of a CO2 laser and study the exchange of thermal energy between the gases. The optically cooled cesium gas efficiently decreases the temperature of the lithium gas through sympathetic cooling. Equilibrium temperatures down to 25 microK have been reached. The measured cross section for thermalizing 133Cs-7Li collisions is 8 x 10(-12) cm(2), for both species unpolarized in their lowest hyperfine ground state. Besides thermalization, we observe evaporation of lithium purely through elastic cesium-lithium collisions (sympathetic evaporation).

Cold atoms and quantum control

This overview prefaces a collection of Insight review articles on the physics and applications of laser-cooled atoms. I will cast this work into a historical perspective in which laser cooling and trapping is seen as one of several research directions aimed at controlling the internal and external degrees of freedom of atoms and molecules.

All-optical formation of an atomic Bose-Einstein condensate

We have created a Bose-Einstein condensate (BEC) of 87Rb atoms directly in an optical trap. We employ a quasielectrostatic dipole force trap formed by two crossed CO2 laser beams. Loading directly from a sub-Doppler laser-cooled cloud of atoms results in initial phase space densities of approximately 1/200. Evaporatively cooling through the BEC transition is achieved by lowering the power in the trapping beams over approximately 2 s. The resulting condensates are F = 1 spinors with 3.5x10(4) atoms distributed between the m(F) = (-1,0,1) states.

Ground state laser cooling using electromagnetically induced transparency

A laser cooling method for trapped atoms is described which achieves ground state cooling by exploiting quantum interference in a driven Lambda-shaped arrangement of atomic levels. The scheme is technically simpler than existing methods of sideband cooling, yet it can be significantly more efficient, in particular when several motional modes are involved, and it does not impose restrictions on the transition linewidth. We study the full quantum mechanical model of the cooling process for one motional degree of freedom and show that a rate equation provides a good approximation.

Suppression of recoil heating by an optical lattice

We report suppression of atomic heating by light scattering due to tight binding in a 3D far-off-resonant optical lattice. We show that rescattered spontaneously emitted photons do not heat trapped atoms when the scattering rate is much less than the trap vibrational frequency.

High resolution feshbach spectroscopy of cesium

We measure high-resolution Feshbach resonance spectra for ultracold cesium atoms colliding in different hyperfine and magnetic sublevels. More than 25 resonances are observed for magnetic fields up to 230 G and their positions are measured with an accuracy down to 0.03 G. From these spectra several ground-state molecular interaction parameters can be extracted with sufficient accuracy to permit for the first time an unambiguous and accurate determination of cesium's ultracold collision properties [P. J. Leo, C. J. Williams, and P. S. Julienne, following Letter, Phys. Rev. Lett. 85, 2721 (2000)].

3D raman sideband cooling of cesium atoms at high density

We laser cool 5x10(7) Cs atoms to a spin-polarized phase space density of 1/30, the highest ever obtained by laser cooling. It is achieved by compression and polarization gradient cooling in a 3D far-off-resonant optical lattice, followed by 3D Raman sideband cooling optimized at a density of 1.5x10(12) atoms/cm(3), and adiabatic release. In the lattice, 23% of the sites are occupied, 95% of the atoms are in the lowest energy magnetic sublevel, and 37% are in the lowest 3D vibrational state.