Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1701.01210 · Physical Review A

High-Compton-frequency, parity-independent, mesoscopic Schrödinger-cat-state atom interferometer with Heisenberg-limited sensitivity

Resham Sarkar, Renpeng Fang, M. S. Shahriar

Published Jul 31, 2018• 10 citations
arXivHTMLPDF

Abstract

We present a protocol for an atomic interferometer that reaches the Heisenberg limit (HL), within a factor of $\ensuremath{\sim}\sqrt{2}$, via collective state detection and critical tuning of one-axis twist spin squeezing. It generates a Schr\"odinger cat state, as a superposition of two extremal collective states. When this Schr\"odinger-cat-state interferometer is used as a gyroscope, the interference occurs at an ultrahigh Compton frequency, corresponding to a mesoscopic single object with a mass of $Nm$, where $N$ is the number of particles in the ensemble, and $m$ is the mass of each particle. For $^{87}\mathrm{Rb}$ atoms, with $N={10}^{6}$, for example, the interference would occur at a Compton frequency of $\ensuremath{\sim}2\ifmmode\times\else\texttimes\fi{}{10}^{31}$ Hz. Under this scheme, the signal is found to depend critically on the parity of $N$. We present two variants of the protocol. Under protocol A, the fringes are narrowed by a factor of $N$ for one parity, while for the other parity the signal is zero. Under protocol B, the fringes are narrowed by a factor of $N$ for one parity, and by a factor of $\sqrt{N}$ for the other parity. Both protocols can be modified in a manner that reverses the behavior of the signals for the two parities. Over repeated measurements under which the probability of being even or odd is equal, the averaged sensitivity is smaller than the HL by a factor of $\ensuremath{\sim}\sqrt{2}$ for both versions of the protocol. We describe an experimental scheme for realizing such an atomic interferometer, and discuss potential limitations due to experimental constraints imposed by the current state of the art, for both collective state detection and one-axis-twist squeezing. We show that when the Schr\"odinger-cat-state interferometer is configured as an accelerometer, the effective two-photon wave vector is enhanced by a factor of $N$, leading to the same degree of enhancement in sensitivity. We also show that such a mesoscopic single object can be used to increase the effective base frequency of an atomic clock by a factor of $N$, with a sensitivity that is equivalent to the HL, within a factor of $\ensuremath{\sim}\sqrt{2}$.

DOI
10.1103/physreva.98.013636

Related papers

Enhancing Sensitivity of an Atomic Interferometer to the Heisenberg Limit Using Increased Quantum Noise

Renpeng Fang

In a conventional atomic interferometer employing $N$ atoms, the phase sensitivity is at the standard quantum limit: $1/\sqrt{N}$. Using spin-squeezing, the sensitivity can be increased, either by lowering the quantum noise or via phase amplification, or a combination thereof. Here, we show how to increase the sensitivity, to the Heisenberg limit of $1/N$, while increasing the quantum noise by $\sqrt{N}$, thereby suppressing by the same factor the effect of excess noise. The protocol uses a Schrodinger Cat state representing a superposition of two collective states of $N$ atoms, behaving as a single entity with an $N$-fold increase in Compton frequency. The resulting $N$-fold phase magnification is revealed by using atomic state detection instead of collective state detection. We also show how to realize an atomic clock based on such a Schrodinger Cat state, with an $N$-fold increase in the effective transition frequency. We discuss potential experimental constraints for implementing this scheme, using one axis twist squeezing employing the cavity feedback scheme, and show that the effects of cavity decay and spontaneous emission are highly suppressed. We find that the maximum improvement in sensitivity can be close to the ideal limit, for as many as ten million atoms.

•Jan 1, 2018•4 citations

Ultra-high Compton Frequency, Parity Independent, Mesoscopic Schroedinger Cat Atom Interferometer with Heisenberg Limited Sensitivity

Resham Sarkar, Renpeng Fang, M. S. Shahriar

We show that collective-state detection combined with one-axis-twist squeezing and un-squeezing can produce a parity-independent, mesoscopic Schroedinger cat atom interferometer with ultra-high Compton frequency, yielding the ultimate (Heisenberg limited) sensitivity allowed by quantum mechanics.

Conference on Lasers and Electro-Optics•Jan 1, 2017•0 citations

Enhancing the sensitivity of an atom interferometer to the Heisenberg limit using increased quantum noise

Renpeng Fang, Resham Sarkar, M. S. Shahriar

In a conventional atomic interferometer employing N atoms, the phase sensitivity is at the standard quantum limit: 1 / N . Under usual spin squeezing, the sensitivity is increased by lowering the quantum noise. It is also possible to increase the sensitivity by leaving the quantum noise unchanged while producing phase amplification. Here we show how to increase the sensitivity, to the Heisenberg limit of 1 / N , while increasing the quantum noise by N and amplifying the phase by a factor of N . Because of the enhancement of the quantum noise and the large phase magnification, the effect of excess noise is highly suppressed. The protocol uses a Schrödinger cat state representing a maximally entangled superposition of two collective states of N atoms. The phase magnification occurs when we use either atomic state detection or collective state detection; however, the robustness against excess noise occurs only when atomic state detection is employed. We show that for one version of the protocol, the signal amplitude is N when N is even, and is vanishingly small when N is odd, for both types of detection. We also show how the protocol can be modified to reverse the nature of the signal for odd versus even values of N . Thus, for a situation where the probability of N being even or odd is equal, the net sensitivity is within a factor of 2 of the Heisenberg limit. Finally, we discuss potential experimental constraints for implementing this scheme via one-axis-twist squeezing employing the cavity feedback scheme, and show that the effects of cavity decay and spontaneous emission are highly suppressed because of the increased quantum noise and the large phase magnification inherent to the protocol. As a result, we find that the maximum improvement in sensitivity can be close to the ideal limit for as many as 10 million atoms.

arXiv:1707.08260•Journal of the Optical Society of America B•May 14, 2020•10 citations

Phase-Amplified Direct Detection of Atomic States for Heisenberg Limited Sensitivity in an Atomic Interferometer Employing Schroedinger Cat States

M. S. Shahriar, Renpeng Fang, Resham Sarkar

In a conventional atomic interferometer employing $N$ atoms, the phase sensitivity is at the standard quantum limit: $1/\sqrt{N}$. Using spin-squeezing, the sensitivity can be increased, either by lowering the quantum noise or via phase amplification, or a combination thereof. Here, we show how to increase the sensitivity, to the Heisenberg limit of $1/N$, while increasing the quantum noise by $\sqrt{N}$, thereby suppressing by the same factor the effect of excess noise. The protocol uses a Schrodinger Cat state representing a superposition of two collective states of $N$ atoms, behaving as a single entity with an $N$-fold increase in Compton frequency. The resulting $N$-fold phase magnification is revealed by using atomic state detection instead of collective state detection. We also show how to realize an atomic clock based on such a Schrodinger Cat state, with an $N$-fold increase in the effective transition frequency. We discuss potential experimental constraints for implementing this scheme, using one axis twist squeezing employing the cavity feedback scheme, and show that the effects of cavity decay and spontaneous emission are highly suppressed. We find that the maximum improvement in sensitivity can be close to the ideal limit, for as many as ten million atoms.

•Jul 26, 2017•0 citations

N -atom collective-state atomic interferometer with ultrahigh Compton frequency and ultrashort de Broglie wavelength, with N reduction in fringe width

Resham Sarkar, May E. Kim, Renpeng Fang +1 more

We describe a collective-state atomic interferometer (COSAIN) with the signal fringe as a function of phase difference or rotation narrowed by $\sqrt{N}$ compared to a conventional interferometer, $N$ being the number of atoms, without entanglement. This effect arises from the interferences among collective states, and is a manifestation of interference at a Compton frequency of $10\phantom{\rule{0.16em}{0ex}}\ifmmode\times\else\texttimes\fi{}\phantom{\rule{0.16em}{0ex}}{10}^{30}$ Hz, or a de Broglie wavelength of 4.5 femtometer, for $N={10}^{6}$ and $v=1$ m/s. The population of the collective state of interest is detected by a null measurement scheme, in which an event corresponding to detection of zero photons corresponds to the system being in that particular collective state. The signal is detected by collecting fluorescence through stimulated Raman scattering of Stokes photons, which are emitted predominantly against the direction of the probe beam, for a high enough resonant optical density. The sensitivity of the ideal COSAIN is found to be given by the standard quantum limit. However, when detection efficiency and collection efficiency are taken into account, the detection scheme of the COSAIN increases the quantum efficiency of detection significantly in comparison to a typical conventional Raman atomic interferometer employing fluorescence detection, yielding a net improvement in stability by as much as a factor of 10. We discuss how the inhomogeneities arising from the nonuniformity in experimental parameters affect the COSAIN signal. We also describe an alternate experimental scheme to enhance resonant optical density in a COSAIN by using cross-linearly polarized counterpropagating Raman beams.

arXiv:1410.7131•Physical Review A•Dec 7, 2015•7 citations

Rapid Generation of a Macroscopic Schrödinger Cat State of Atoms with Parity-Independent Orientation

Li, Jinyang, Gregório R. M. da Silva, Schuyler Kain +1 more

We show that using the process of one-axis-twist squeezing in an echo configuration, it is possible to control the orientation of the macroscopic magnetic moment of a large number of atoms by manipulating the quantum state of a single atom that is physically isolated from the ensemble. With this control technique, it is also possible to entangle an ensemble with a single atom deterministically, which mimics the thought experiment known as the Schrödinger cat. In addition, this technique would make it possible to generate a mesoscopic Schrödinger cat state for a large number of atoms far more rapidly that the conventional process for generating such a state, with an orientation that is independent of the parity of the number of atoms. Apart from the echo configuration, we have also investigated the behavior of one-axis-twist squeezing for some special values of the squeezing parameter. We find that the squeezing propagator can be expressed as the sum of n rotation operators if the product of n and the squeezing parameter equals pi, where n is a non-zero integer. A direct consequence of this property of one-axis-twist squeezing is that there is a hidden order in a squeezed state generated under this condition even if its Husimi quasi-probability distribution looks irregular.

arXiv:2210.15115•Oct 27, 2022•0 citations
We present a protocol for an atomic interferometer that reaches the Heisenberg limit (HL), within a factor of \ensuremath∼2\ensuremath{\sim}\sqrt{2}\ensuremath∼2​, via collective state detection and critical tuning of one-axis twist spin squeezing. It generates a Schr"odinger cat state, as a superposition of two extremal collective states. When this Schr"odinger-cat-state interferometer is used as a gyroscope, the interference occurs at an ultrahigh Compton frequency, corresponding to a mesoscopic single object with a mass of NmNmNm, where NNN is the number of particles in the ensemble, and mmm is the mass of each particle. For 87Rb^{87}\mathrm{Rb}87Rb atoms, with N=106N={10}^{6}N=106, for example, the interference would occur at a Compton frequency of \ensuremath∼2\ifmmode×\else\texttimes\fi1031\ensuremath{\sim}2\ifmmode\times\else\texttimes\fi{}{10}^{31}\ensuremath∼2\ifmmode×\else\texttimes\fi1031 Hz. Under this scheme, the signal is found to depend critically on the parity of NNN. We present two variants of the protocol. Under protocol A, the fringes are narrowed by a factor of NNN for one parity, while for the other parity the signal is zero. Under protocol B, the fringes are narrowed by a factor of NNN for one parity, and by a factor of N\sqrt{N}N​ for the other parity. Both protocols can be modified in a manner that reverses the behavior of the signals for the two parities. Over repeated measurements under which the probability of being even or odd is equal, the averaged sensitivity is smaller than the HL by a factor of \ensuremath∼2\ensuremath{\sim}\sqrt{2}\ensuremath∼2​ for both versions of the protocol. We describe an experimental scheme for realizing such an atomic interferometer, and discuss potential limitations due to experimental constraints imposed by the current state of the art, for both collective state detection and one-axis-twist squeezing. We show that when the Schr"odinger-cat-state interferometer is configured as an accelerometer, the effective two-photon wave vector is enhanced by a factor of NNN, leading to the same degree of enhancement in sensitivity. We also show that such a mesoscopic single object can be used to increase the effective base frequency of an atomic clock by a factor of NNN, with a sensitivity that is equivalent to the HL, within a factor of \ensuremath∼2\ensuremath{\sim}\sqrt{2}\ensuremath∼2​.
In a conventional atomic interferometer employing NNN atoms, the phase sensitivity is at the standard quantum limit: 1/N1/\sqrt{N}1/N​. Using spin-squeezing, the sensitivity can be increased, either by lowering the quantum noise or via phase amplification, or a combination thereof. Here, we show how to increase the sensitivity, to the Heisenberg limit of 1/N1/N1/N, while increasing the quantum noise by N\sqrt{N}N​, thereby suppressing by the same factor the effect of excess noise. The protocol uses a Schrodinger Cat state representing a superposition of two collective states of NNN atoms, behaving as a single entity with an NNN-fold increase in Compton frequency. The resulting NNN-fold phase magnification is revealed by using atomic state detection instead of collective state detection. We also show how to realize an atomic clock based on such a Schrodinger Cat state, with an NNN-fold increase in the effective transition frequency. We discuss potential experimental constraints for implementing this scheme, using one axis twist squeezing employing the cavity feedback scheme, and show that the effects of cavity decay and spontaneous emission are highly suppressed. We find that the maximum improvement in sensitivity can be close to the ideal limit, for as many as ten million atoms.
In a conventional atomic interferometer employing N atoms, the phase sensitivity is at the standard quantum limit: 1 / N . Under usual spin squeezing, the sensitivity is increased by lowering the quantum noise. It is also possible to increase the sensitivity by leaving the quantum noise unchanged while producing phase amplification. Here we show how to increase the sensitivity, to the Heisenberg limit of 1 / N , while increasing the quantum noise by N and amplifying the phase by a factor of N . Because of the enhancement of the quantum noise and the large phase magnification, the effect of excess noise is highly suppressed. The protocol uses a Schrödinger cat state representing a maximally entangled superposition of two collective states of N atoms. The phase magnification occurs when we use either atomic state detection or collective state detection; however, the robustness against excess noise occurs only when atomic state detection is employed. We show that for one version of the protocol, the signal amplitude is N when N is even, and is vanishingly small when N is odd, for both types of detection. We also show how the protocol can be modified to reverse the nature of the signal for odd versus even values of N . Thus, for a situation where the probability of N being even or odd is equal, the net sensitivity is within a factor of 2 of the Heisenberg limit. Finally, we discuss potential experimental constraints for implementing this scheme via one-axis-twist squeezing employing the cavity feedback scheme, and show that the effects of cavity decay and spontaneous emission are highly suppressed because of the increased quantum noise and the large phase magnification inherent to the protocol. As a result, we find that the maximum improvement in sensitivity can be close to the ideal limit for as many as 10 million atoms.
In a conventional atomic interferometer employing NNN atoms, the phase sensitivity is at the standard quantum limit: 1/N1/\sqrt{N}1/N​. Using spin-squeezing, the sensitivity can be increased, either by lowering the quantum noise or via phase amplification, or a combination thereof. Here, we show how to increase the sensitivity, to the Heisenberg limit of 1/N1/N1/N, while increasing the quantum noise by N\sqrt{N}N​, thereby suppressing by the same factor the effect of excess noise. The protocol uses a Schrodinger Cat state representing a superposition of two collective states of NNN atoms, behaving as a single entity with an NNN-fold increase in Compton frequency. The resulting NNN-fold phase magnification is revealed by using atomic state detection instead of collective state detection. We also show how to realize an atomic clock based on such a Schrodinger Cat state, with an NNN-fold increase in the effective transition frequency. We discuss potential experimental constraints for implementing this scheme, using one axis twist squeezing employing the cavity feedback scheme, and show that the effects of cavity decay and spontaneous emission are highly suppressed. We find that the maximum improvement in sensitivity can be close to the ideal limit, for as many as ten million atoms.
We describe a collective-state atomic interferometer (COSAIN) with the signal fringe as a function of phase difference or rotation narrowed by N\sqrt{N}N​ compared to a conventional interferometer, NNN being the number of atoms, without entanglement. This effect arises from the interferences among collective states, and is a manifestation of interference at a Compton frequency of $10\phantom{\rule{0.16em}{0ex}}\ifmmode\times\else\texttimes\fi{}\phantom{\rule{0.16em}{0ex}}{10}^{30}$ Hz, or a de Broglie wavelength of 4.5 femtometer, for N=106N={10}^{6}N=106 and v=1v=1v=1 m/s. The population of the collective state of interest is detected by a null measurement scheme, in which an event corresponding to detection of zero photons corresponds to the system being in that particular collective state. The signal is detected by collecting fluorescence through stimulated Raman scattering of Stokes photons, which are emitted predominantly against the direction of the probe beam, for a high enough resonant optical density. The sensitivity of the ideal COSAIN is found to be given by the standard quantum limit. However, when detection efficiency and collection efficiency are taken into account, the detection scheme of the COSAIN increases the quantum efficiency of detection significantly in comparison to a typical conventional Raman atomic interferometer employing fluorescence detection, yielding a net improvement in stability by as much as a factor of 10. We discuss how the inhomogeneities arising from the nonuniformity in experimental parameters affect the COSAIN signal. We also describe an alternate experimental scheme to enhance resonant optical density in a COSAIN by using cross-linearly polarized counterpropagating Raman beams.
We show that using the process of one-axis-twist squeezing in an echo configuration, it is possible to control the orientation of the macroscopic magnetic moment of a large number of atoms by manipulating the quantum state of a single atom that is physically isolated from the ensemble. With this control technique, it is also possible to entangle an ensemble with a single atom deterministically, which mimics the thought experiment known as the Schrödinger cat. In addition, this technique would make it possible to generate a mesoscopic Schrödinger cat state for a large number of atoms far more rapidly that the conventional process for generating such a state, with an orientation that is independent of the parity of the number of atoms. Apart from the echo configuration, we have also investigated the behavior of one-axis-twist squeezing for some special values of the squeezing parameter. We find that the squeezing propagator can be expressed as the sum of n rotation operators if the product of n and the squeezing parameter equals pi, where n is a non-zero integer. A direct consequence of this property of one-axis-twist squeezing is that there is a hidden order in a squeezed state generated under this condition even if its Husimi quasi-probability distribution looks irregular.